Yes, bednobs, it occurred to me after I'd posted that I'd managed to avoid answering your question entirely! :(
They are, at the very least, somewhat related, as gender identity and sexual identity are in the first place often linked together by people as one and the same, even if they actually aren't. And, in a crude (and not always accurate) way, both typically involve what you do, or want to do, with what's inside your pants...
Also the "T" in LGBT often covers multiple gender-identity-related aspects, eg transvestism and so on, so it could be regarded as the sort of "anything that's different from heterosexual and cisgender" part of gender and sexual identity. I think they do belong together, sort of.