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 fly, hop, and pump in a fast, forward way. Carbon fiber does not like vertical drops or hard abuse. Race bikes are specialized and designed to their discipline. You don't need a race bike to start racing, but it helps if you plan to keep racing.
Freestyle is a generic term encompassing a few styles like vert, park, and flat. BMX started as racing, and doing tricks was just a natural growth. In the 80's the design split between race bike and freestyle bike happened. Freestyle bikes are heavier duty meant for smashing, grinding, jumping, vertical air, and doing crazy (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
Compare the frame angles
Designed for race tracks
Steel frame
Heavier, thicker tires
Micro gearing to keep it out of the way
Compare the frame angles
Designed for skate parks