Track bikes are designed to be fast on a smooth, banked surface; a place where brakes are not needed and indeed are dangerous to use. Very responsive, twitchy handling.

The things that make a track bike excel on the track make it a poor bike for riding on city streets or out in the country on the open road. Likewise, a road bike isn't built for the track.

Road geometry varies from company to company and from "racer" geometry to "recreational" geometry. The more agressive ones approach track geometry but still have a longer wheelbase and more trail which gives them more stability; a good thing on fast descents down mountains. Time trial bikes are basically track bikes with gears and brakes and aero bars. Touring bikes have even longer wheelbases, more trail, slacker headtube and seattube angles. They are designed to carry a lot of weight and still be stable.

Subtle changes in the tube angles and lengths can greatly affect the way a bike feels and rides so it is a good idea to test ride lots of bikes before deciding on one.

Unless it's a track bike, where only fashion sense rules.