There are two basic types of BMX bike:
Race
Park/Freestyle/Flat/Vert/Ramp/Street
Racing is racing. Race bikes are light, fast, and will not do tricks. They jump and pump in a fast, forward way. Carbon fiber does not like vertical drops or hard abuse. Race bikes are more specialized. You don't need a race bike to start racing, but it sure helps.
Freestyle is a broad term encompassing trick styles. BMX started as racing, and trick riding was a natural growth. In the 80's the split between race bike and freestyle bike became more pronounced. Freestyle bikes are heavy duty meant for smashing, grinding, jumping, vert air, and doing dumb things in skateparks (we'll admit it if you admit it). You can race a freestyle bike and it's fun, but they tend to be slower and will want to jump everything since they were designed to do that.
Race Bike
Park/Freestyle Bike
Aluminum frame
Lighter, thinner tires
Customizable gearing
Rider position forward
Compare the frame angles
Designed for race tracks
Steel frame
Heavier, thicker tires
Micro gearing to keep it out of the way
Rider position upright
Compare the frame angles
Designed for skate parks