穿上 emphasizes the action of putting clothes on. 穿着 (chuānzhe) describes the state of wearing. Compare: 他穿上了外套 (He put on a coat) vs. 他穿着外套 (He is wearing a coat).
usage
The opposite is 脱下 (tuōxià, to take off): 穿上外套 (put on a coat) ↔ 脱下外套 (take off a coat).