I am presenting each of these theories from a trans point of view. I know this will seem biased, but trans points of views are often neglected when others talk about how to examine gender.
There is no perfect gender theory yet. Each perspective explains some things well and cannot explain others. There are few purists that cling solely to a single theory. Many people recognize that there is no one of these theories that explain all their experiences or what they see in their lives. Each theory has important contributions to our understanding of gender. I think gender is far more complex than any of these theories. I believe these theories should be studied to see the perspectives people use to view gender rather than describe the intricacies of the gender system as it exists.
Before we can even think about looking at gender, we must know what gender is and how it differs from sex.
For the purpose of this article, sex is a set of categories used to describe biological and physical traits. It is internal and external organs, chromosomes, hormone levels, genitalia etc.
Gender is in one's mind, spirit and soul. It is the gendered sense of one being. Gender is often described as masculine, feminine, woman and man.
Gender means different things to different people. Your definition of gender often directs the way you look at gender. One common perspective of gender focuses on roles, while another focuses on identity.
If you define gender as an identity, then you are more likely to look at how that identity is formed and the implications of the formation of that identity. Someone might look at whether the identity is innate or constructed. If it is constructed then you look at how is it constructed both as an individual and as culture and how it influences your existence and how you view yourself.
If you focus on gender as a set of roles you are more likely to look at how those roles are constructed both as an individual and as a culture and the implications on your existence.
The range of meanings the word "gender" can take creates a real dilemma. It is difficult not to use the word gender unqualified. This means we need a few more definitions to define things people often refer to when they say gender.
Gender identity is how you see yourself socially and how you see yourself interacting in the world that we live in: man, woman, neither, combination of both or fluidly relating as one and then the other.Looking at gender as an identity looks at how we defined ourselves and the meanings it creates in our lives.
Gender Role is the set of social expectations based on gender stereotypes of what how a person should act, think and feel based on their actual or perceived sex. Our society assumes men perform the masculine role and women perform the feminine role.
Gender expression is the gendered traits one expresses. It can be congruent or incongruent with one's identity or the roles society has prescribed for the individual.
NOTE: Generally, I use male and female to denote sex; masculine and feminine to denote gender expression; and man and woman to denote gender identity and gender roles.
Sandy Stone (Allucquere Rosanne Stone) summarizes an essentialist as:
Essentialists believe that sex and gender are the same thing, or at any rate inseparable. Both arise from "nature" or are "God-given". Chromosomal characteristics, visible sex markers (penis, vagina), and gender cannot be separated. Essentialists usually believe that there are only two genders; these are present at birth; remain unchanged for life; and there is no territory between. Behaviors or appearances that do not fit these assumptions are viewed as "perversions".
Reverse Essentialist believe in essentialism, but use it to present the strengths of the traditionally devalued role(s) and/or identities. They stress differences that are thought to be innate and focus on how the group(s) that are traditionally less valued have traits that are valuable.
Semi-essentialist view only part of gender (usually gender identity) as innate while recognizing other aspects of gender as constructed. This allows someone to have an essential gender identity while exploring the constructed nature of gender roles.
Sandy Stone defines a social constructionist as:
Social constructivists believe that both sex and gender arise in social interaction and have no existence independent of social interaction; i.e., they are not grounded in "nature", the meaning of which is itself socially determined. The "constructedness" of sex and gender is made invisible by the normal workings of social life, so that they appear natural rather than artificial. Recent constructivist theory also points out that the idea of two absolute chromosomal sexes is also a social construction. Recall the film Alien 3, in which the inhabitants of the prison colony are all double-Y chromosomal; thus although they possess many of the secondary sexual characteristics of males, genetically they are not male, nor are they any other category for which we currently have a socially understood name. (Heartfelt thanks again, Ridley!)
There belief that gender roles, gender identity, and sex are socially constructed opens a large number of new questions as you analyze the social construction of sex and gender identity as well as the social construction of gender roles.
While it is much more, people relate social constructionism to social learning theory from psychology. Social learning theory would say that men and women behave as they do because they are taught through society the way men and women behave.
Sandy Stone defines a performance theorist as:
Gender performance theorists believe that gender is performed like any theatre work, is independent of sex, and is best understood through performance studies. Performance has been seized on most productively by political activists to make visible the structure of the performance (body position, gesture, facial expression, proxemics, voice modulation, speech pattern, social space, markers of clothing, adornment and cosmetics) and to point up its artificial quality in direct ways.
While Riki Wilchins sums up one of the fundamentals ideas of performance theory in her definition of real: "REAL. What any gender is until the exact moment you become aware you're performing it - then it becomes drag." his illustrates how performance theorists analyze gender as performed.
Sandy Stone summarizes Memory and Language Generation Theory in this way:
In this thread the body is a central node and apparatus for meaning production in a complex system of symbols and their exchange that we commonly call language. However, rather than simply being a passage point for always-already socially understood symbols, the body is a source of new symbols which are taken up by social networks and incorporated into a larger cultural language which includes words and gestures but is not limited to them. The body is also linked to deeper knowledges which cannot be expressed through text or sound and that originate before the growing child learns to verbalize or to gesture. One of the characters in my novel repeatedly says, "The body remembers. Not the mind. The body."
This perspective looks at how we as individuals create meaning around bodies. Meaning is created by linking a signifier "something that means something to someone" to the signified. Thus bodies and parts of bodies take on personal and socially understood meanings.
Interval demotic theory is not a theory proper, but rather a variation of a theory. Memory and Language Generation Theory and Performance Theory dictates that all meaning is constructed through the use of signifiers and the signified. This creates a system that obscures the social relationships making aspects like power, privilege and social agency hard to see. These were clearly things that we wanted to look at and discuss, but without resorting to a system of binary dualities (real/artificial, essential/constructed, etc.) that social construction tended to lead us to.
Interval-demotics looks at the different spheres of influence that have been constructed and how they are separated, yet have a relationship. Thus a single person individually constructs what gender means and a cultural group collectively constructs what gender means. Interval-demotics looks at the way in which the realms are constructed and relationship between those two constructions within those realms. Thus it can highlight privilege, power and social agency in new ways (All things that are difficult to examine under memory and language generation theory).
While interval-demotics was created by memory and language generation theorist it has been applied to social construction, looking at the hierarchy of social levels and construction; and performance theory, looking at the different "stages" that gender is performed on and the relationship between those performances.
For this discussion I will look at gender expression (It's the easiest view of gender to illustrate the point.
If someone where to see gender expression as a binary set of categories,
they might see gender something like this:

Seeing gender as a binary continuum you might see gender something like
this:
Seeing gender as a continuum allows someone to be a blend of masculine and feminine. It implies that someone who expresses themself androgenously expresses themself less masculinely than someone whose expression is masculine and less femininely than someone whose expression is feminine.
Lets say that we define masculine expression as that which shows agency:
(i.e. assertiveness, agression, action, etc) and that we define feminine
expression as that which shows communion (i.e. caring, clinginess, concern).
Then you might view gender expression something like this:
This allows not only for gender expression to be either/or, but it also allows gender expression to be both/and (or even neither).
I defined feminine expression as communion aand masculine expression as agencies. In doing so I constructed both axis used to describe gender. Some people see the basic concepts which we use to describe gender as constructed.
Just as you could view expression as a binary, binary continuum, multidomension or completely constructed, so you could do the same with sex, gender identity, gender roles, gender attribution, and gender __________ (fill in the blank).
The purpose of me writing this was not to tell you what gender is or how you should view gender. I wrote this just to point out the many complexed ways that people view gender. When we recognize the many different ways of viewing gender we recognize the many diverse perspectives of those that look at gender.