When both boys and girls go through puberty there's a surge in the testosterone levels which activate the sebaceous gland, or the oil gland to make more oil. This is sort of what sets off teenage acne. Teenage acne is most commonly seen in the t-zone. Furthermore, teenage acne is considered a normal part of puberty and it tends to go away.
Adult acne tends to happen especially to women in their 20's and 30's and may not be caused by too much of a hormone but by a hormonal imbalance. And this is why it's so often treated with things that modulate your hormones. Unlike teenage acne which occurs in the t-zone, adult acne in women tends to occur in the lower half of the face, the chin, the jaw, and the neck. And thus would need different kinds of treatments than teenage acne.
Finally I find that I can use much harsher treatments in my teenagers than I can in my adult women who's skin gets much more sensitive. So many adults will be acne despite not having oily skin. And that differs from teenagers as well.