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Crossdressers are real and can (technically) be male or female; though nobody really cares anymore if women wear jeans a t-shirts. Usually though, it means a man dressing as a woman. Even the best crossdressers can rarely "pass" as real women because usually they aren't trans (on hormones) so have a masculine body/face, especially if they are older than their teens.
Traps are an anime meme and are always men, usually very young men (sometimes kids). Because they are fictional characters, they can look identical to females and nobody can tell the difference. In other words, it's literally just a female that you're supposed to believe is a male, or in some cases a female with a dick.