Drill Bits
Technically, a drill bit is a reamer. However, drill bits are a more generalized tool, primarily used to remove material or drill a hole completely through material to the other side. Drill bits are very efficient at removing material quickly, but they have a tendency to "walk," which means they may not drill a perfectly perpendicular hole, even when used in a drill press or vertical mill -- or they may not drill a hole exactly were the bit first touches material; the spiral tip walks away from the starting point and doesn't track on axis. Vertical reamers are specialized tools that do what most drill bits can't.
Reamers
Reamers differ from drills in a number of ways. Where drills are very effective at removing a lot of material quickly, reamers are effective at cutting the outside diameter of a hole very precisely. With the bulk of material removed by a drill, the reamer can center the hole, perfectly on axis.
Cutting Surfaces
Where drills are designed to cut from the tip, then channel shavings through their flutes, reamers are designed to cut from the sides. They also have flutes, but not the tight-spiraled flutes of drill bits.
Use With Pilot Holes
Where the tip of a drill bit is designed to cut into solid material, true vertical reamers are designed to be used in conjunction with a drill bit. The reamer has a more sturdy, solid central shaft that effectively eliminates bit-flex and "walk"; the trade-off is that the central mass of the hole has to be removed before the precision reamer -- whether it's used in a vertical mill, drill press, or even a hand drill -- can tidy up the walls of the hole.