Well things get complicated here IMO. According to a LOT of people, what you described is the ?real? definition of crossdressing. A lot of people consider crossdressing specifically the act of dressing in the opposite gender clothes for sexual gratification. Everyone else would be a trans person expressing their gender.
Of course there is going to be a chorus of people here who say ?Wait a minute! I dress to express but Im a crossdresser and NOT trans!?
The bottom line is that most of the vocabulary surrounding our community is currently in transition and flux, so don?t worry too much about the ?proper? terminology because the whole world is still trying to figure that out.