I thought Trans and gay are two different things.
They are. The get confused because
some gay people are quite like the opposite sex. It's really confusing because research has suggested polar opposites. One bit of research showed that the brains of gay people are somewhat hybrid between the two sexes while other research suggested that gay men can be exposed to
higher levels of testosterone in the womb. And, some research has found that gay men tend to pair up in terms of a masculine partner and less masculine partner, just as the old offensive-to-most stereotype of "Who is the man and who is the woman?" suggested would be true. It may be that some gay men are biologically more feminine than the average hetero men while others are biologically more masculine. Nature is complicated.
The thing about transgenderism, though, is that a transgendered person is, in one key respect, the opposite of a gay person. While a gay person loves their sex a trans person doesn't. It's a very different experience. Only gay people can really experience the feeling of being attracted to their own bodies to a high degree. It's a unique aspect of being gay and something that has been recognized since humanity started (e.g. Narcissus). Trans and hetero people don't have that. Trans people are the furthest from it, wanting to have their bodies changed to the opposite sex.
Of course, there are gay people who seems trans (those who don drag beyond something for the occasional Halloween party) and hetero people who like to crossdress. Gender is complicated. Hetero men who crossdress, for instance, are typically more macho/masculine in look and behavior than the average hetero man.