Join Date: Jun 2013
Location: Cedar Rapids, IA
Bikes: 1997 Rivendell Road Standard 650b conversion (tourer), 1988 Schwinn Project KOM-10 (gravel/tour), 2013 Foundry Auger disc (gravel), 2016 Cannondale Fat CAAD 2 (MTB/winter)
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Always ask Sheldon, He Has The Answer
Caliper brakes are sidepull (dual or single pivot). They mount to the hole in the fork crown. They're light, easy to install/adjust. But they have limited tire/fender clearance, for the most part.
Cantilever brakes mount to specific posts (bosses) on the fork legs/stays. They don't limit the tire clearance, which is why they were on touring and mountain bikes for years. Harder to install/adjust, and they require a hanger.
Direct-pull brakes (linear-pull, or V-brakes) mount to cantilever brake posts. They dont' limit the tire clearance. They are easier to install/adjust than cantilevers. Some claim they don't work as well, many find them ugly. They require different brake levers than the above brakes (they pull a different amount of cable to function).
There are also centerpull brakes, that are kind of between sidepull and cantilever brakes.
Disc brakes are totally different, and require specific braces built into the frame.