Is transgenderism similar to BIID? Please read ALL the details.

In my studies, I learned about Body Identity Integrity Disorder. This a rare condition where people do not identify with part of their body, or a function of it. Example include people who believe they should be an amputee, or paraplegic. It isn’t a wish, they truly don’t identify with the body part, and will go to extreme lengths to get rid of the offending body part.

I’ll readily admit that I don’t understand transgenderism, and I don’t personally know any people who identify as transgender. So I am asking the question for the purpose of learning, not judging. But reading about BIID reminds me of transgenderism in that people feel that their body (and the genetics that formed their body) does not reflect their identity. They also take physical steps to appear as they feel they are, i.e. unnecessarily using a wheelchair in BIID, or crossdressing in transgenderism.

Is this an appropriate comparison? Could it help us understand either case better?