The difference is the acceptance of society, the peer pressure disapproval, Quiz. When jeans and trouser suits became acceptable for women then they were 'allowed' by society to cross dress with impunity. And now it is no longer anything to note. As usual, the same freedoms were not made available to the men. But the lack of equal treatment isn't the issue here. It's why some feel the need to do so.
I don't think it can be reasonably compared to homosexuality, which is to do with sexual partner preference; nor transgender, although I suspect in some cases it may indicate a mild desire to have been born as the other gender, without wishing to go so far as to actually mimic them permanently.