They are not related or comparable to each other at all. Transgenderism refers to gender identity or an umbrella of gender identities, and trans and non-binary people have existed
all throughout human history. Transhumanism is a new movement that seeks to expand human capabilities to their highest potential through use of new and continuously improved technology, to the extent that technology becomes the driving force behind human evolution rather than natural selection.
A trans person doesn't want to expand their physical capabilities, only to match their physical traits (sex) to what they are psychologically (gender).
Extreme body modification doesn't fit into either of those categories, although there are some people who insist that they are actually dogs or cats or lizards and try to match their appearance to such. But that's more of a subculture than an identity.