not necessarily. the communities overlap heavily, which is why they’re grouped together, but “transsexual,” “mtf” and “ftm” were all in use before “transgender,” which is itself a term that dates back to the early ‘60s. (also, please don’t scare quote “trans.”)
We also both have "oppression that is gendered but Not Like That" going on. I know a lot of trans lesbians who had experience being called gay because of effeminacy in their egg days, who were basically at "... but I'm into girls?" about it.
I don't believe they for the most part had gay community connections (unless they had them for ally reasons), but they did have experience of homophobia. And me, I despair sometimes of finding people who talk about trans men who don't assume that we somehow belong in sapphic circles.