How does trading your car work?

Sup guys...I was wondring if tyou guys can help me out on this. Right now I have a 2007 Chevy cobalt LS sedan, it only has 11,000 miles on it. I've had it for about 6 months now, so I still have like 13,500 to still pay off.... Now is there any way I can trade it in for an Acura rsx type-s and not have the payments go up on me cuz right now i pay 400 a month for the Chevy, or does the dealer take my car and take care of the payments while i take over the rsx payments? Sorry, i don't know too much about how that works. I was lookin for an older model maybe like a 2004 type-s with like 60k-70k miles...thanks guys.