
What is a tomboy, exactly?
I participated in a discussion recently about the tomboy character in literature. We discovered that we all had very different opinions of what constituted a tomboy. If you search online these days, you'll find definitions associating tomboys with lesbians and transgenders, which I think is wrongheaded and anachronistic.
I know what I mean when I say tomboy, and I think of it it as an example of a story character archetype which, like all archetypes, reflects something in real life.
Let's try this definition:
A tomboy is a girl or young woman, typically pre-pubescent or at least virginal, who values highly the same male virtues that appeal to boys of her own age, and values less the virtues that appeal to girls of her own age.
With the exception of Jo March (Little Women, Louisa May Alcott), most tomboys in literature are secondary characters: Little Scout (The Keeper of the Bees, Gene Stratton-Porter), Anybody's (West Side Story), Tiger Lily (Peter Pan, J.M. Barrie), Arya Stark (A Song of Ice and Fire, George R.R. Martin) are some relatively recent examples.

I think the age (pre-pubescent or virginal) is an important distinction. The tomboy is not about sexuality, despite the appalling modern tendency to read sex and gender into absolutely everything.
The character Anybody's from West Side Story is, to my thinking, a marginal example. She wants to be one of the Jets, but she bears the brunt of sexual jokes and clearly desires one of the other gang boys.

The warrior maids of folklore, the shieldmaidens of Viking stories, and heroines like Atalanta or goddesses like Athena and Artemis fall into this sphere as well. Both Athena and Artemis are virgin goddesses with male interests (war and hunting), and no one thinks of them sexually with impunity, as Actaeon and others discovered.

When a literary tomboy matures, she turns into an adult heterosexual woman, not a lesbian or transgender. Atalanta marries. Brunhilde marries. Jo March marries. Except for Tiger Lily, in a timeless world, there's no reason to think that the other examples above (Little Scout, Arya Stark) won't marry eventually.
What do tomboys want?
The explicit tradeoff is: I want to be treated like any other boy, and in exchange, I promise not to behave like a girl (cry, complain, whine). They don't want to be boys — they want to behave like boys and earn the respect that boys earn from their peers.
Anybody's and Little Scout have literal gangs to belong to. The reason so many tomboys play alone in real life is that there isn’t a gang around that’ll have them, so they make a virtue (independence) of necessity.
All of this only works until sex comes along to disturb things. The adult version of women being “one of the boys” (as in combat or police careers) is very, very different. There it only works (when it works) when both parties are submerged in “professionalism” (esp. the women).
Tomboys aren’t about being mature professionals — they’re about acquiring virtues as sub-adults do, by contest and ritual and the example of their peers, as they prepare for a rite of passage to adulthood. Tomboys (outside of fiction) don't pass that particular gate with the boys, but they get as close to it as they can.
It’s also about masculine honor codes. Tomboys want to learn about and manifest the masculine virtues of courage, fortitude, and the protection of their brothers-in-arms, not because the virtues are masculine per se, but because they are generally admirable. After all, don’t all the great stories tell us so?
Besides, the traditional male and female virtues are not opposites, but complementaries. Courage being a man’s virtue does not preclude it from being a woman’s also.