I think the confusion is coming from the fact that cis and trans really only have context of an expectation. In this case, it would be the expectation of society.
You are correct that if you identify as a woman or a man, you are a woman or man. If you have a penis, or a vagina, or some mix or lack of those, then those are just parts of your body and that isn't really up to interpretation.
In broad strokes, society expects your body parts (penis, vagina) to correspond to how you identify (man, woman). Humans are kind of just built this way. Our brains take a lot of shortcuts and categorize the world around us. It is statistically likely that if you have a penis, you identify as a man.
As we've evolved as a society, we have come to understand and recognize that these statistically likely correlations not always hold up (it's just likely, not a guarantee, after all). So cis and trans are descriptors of whether or not the correlation between your gender identity and your physical characteristics match (cis) or don't match (trans) society's expectations.