DUI = Driving under the influence.
DWI = Driving while <ability> Impaired.
DUI is the more serious of the two and depending on where you live has stiffer fines and penalties.
In Colorado .10 or greater BAC will earn you a DUI.
.05 up to .09 will get you a DWI. Some states have lowered to .08 and .04. Basically, 2 beers in an hour will put you over the limit, so be careful and take a cab.