I will not cover everything in this post.
Quotation marks indicate a reference to the term rather than the group defined by the term.
Includes terms I found interesting, and a few I made up out of roots that I think should make them fairly clear, occasionally with added syllables for rolling-off-the-tongue value.
EDIT: anthro- terms were previously gynandro-/androgy- terms (see comments).
Sexual identity is complex.
First of all, the standard-use terms currently don't define sexual orientation by what one is attracted to. The axes are what one likes and what one is--and the name is taken from the interaction between the two.
The assumptions are: you are male or female; you like males, females, both, or neither, and romantic attraction and sexual attraction are intrinsically linked. From these priors, we commonly call people homosexual, heterosexual, bisexual, or asexual.*
These assumptions fail upon contact with the world. Not everyone is male or female. There are people who self-identify as both, neither, inconsistent/uncaring, or somewhere along a spectrum; there are hormone differences that set people along many parts of the spectrum; and even if we limit it to viable combinations of the X and Y chromosomes that science has formally observed, there are more than two options. Any way you care to slice it, a male/female dichotomy doesn't work.
So we've already found that 'hetero-/homosexual' don't work, because they rely on defined genders/sexes to work--you are attracted to something like you, or something distinct from you. 'Bisexual' does not work because 'bi' means 'two', so if we have more than two genders/sexes--never mind a spectrum--the term starts being rather absurd. Even if there were only two, I would prefer 'ambisexual' rather than 'bisexual', that is 'both' rather than 'two', but that's neither here nor there.
Given only the breakdown of strictly defined self-identity, asexual still works. 'A' simply means 'none', and the fact that it may originally have been meant as 'neither' does no harm to the term.
I will now use 'gynosexual', 'androsexual', and 'anthrosexual' for--respectively--attraction to feminine traits, masculine traits, and humans, and keep 'asexual'.
The added complexity doubles in attraction. I have already made the point that being attracted to a female or a male is not quite the same as being attracted to feminine or masculine traits. It is also possible to be attracted to the idea of a person being male/female, much as one can be attracted to the idea of someone being intersex.
Then there's the point that romantic attraction and physical attraction are not so perfectly snapped together. One can be, for example, asexual but andromantic--that is, lacking in a sexual drive, but still having a desire to be romantically involved with males/people with masculine traits.
* Other terms exist, but are much less common.To see how complicated this gets in practice, I will refer to a previous post. The focus question: "Is Abby/Maggie a lesbian relationship?"
Strictly speaking, neither Maggie nor Abby have set genders/sexes--that is to say, they lack chromosomes altogether, and appear as whatever they want to look like during that slice of time.
Maggie has chosen a female form because that is what she feels she is. She is also attracted to feminine traits--she is gynosexual--is romantically attracted to people who are female/feminine--gynoromantic--and is attracted to the idea of someone being female. In other words, Maggie is a pretty classic lesbian. One could quibble that Maggie could choose to be male or sexless, but that's splitting some pretty fine hairs.
Abby, on the other hand... Abby likes Maggie. This does not spread to sexual love, but that's not because Abby doesn't find Maggie attractive; it's because Abby hasn't bothered to manufacture a sex drive for herself. Maggie was a creative force, so had a bit of one, and honed it because she wanted to, but entropy would have needed to create one from the ground up, and didn't care enough to manipulate one into being. This makes Abby asexual: it's not that she finds sex repulsive, she just doesn't particularly care about it. Romantically, Abby is attracted to traits, independent of the gender/sex of the being. This makes her anthromantic. Abby chose a vaguely female form and influenced Maggie with some positive bias because she recognized that Maggie would find a female/feminine form more attractive, and because Abby cares about as much about her form as about her partner's.
From Maggie's perspective, it's obviously a lesbian relationship. From Abby's perspective, it's a romantic relationship, and she'd probably look at you oddly if you tried to push gender/sex into it. If given the choice between a lesbian relationship, a heterosexual relationship, a male-homosexual relationship, and a polyamorous relationship, Abby would call it lesbian. But that's not a good description; it is merely better than the other three options.
All in all, I just try to stick with 'romantic,' 'sexual,' and 'relationship.'