As others have said, driving is more important here than in some other countries (as many of us live more spread out), so it makes sense to have a lower driving age, out of necessity. On the other hand, young drivers and easily available alcohol don't mix well, and drinking is of course less of a necessity than driving, so a slightly higher drinking age makes sense too. The drinking age was 18 until the '80s, and drunk driving incidents did decrease -- by some estimates, quite substantially.

And for the record, the drinking age is fairly porous. In most states, it's actually the purchase of alcohol by 18-year-olds that's prohibited, and drinking in some circumstances (e.g. with of-age family members) is permitted. And drinking by college students, even below 21, is pretty much ubiquitous. The biggest effect of the 21-year age limit seems to be more to keep alcohol out of the hands of even younger people, like 15-16.