Understanding the three basic types of distances on FFH will help you in many ways. This will allow you to determine at what distances your horse will run best. Horses will train faster at the distances their genes determine. Those genes will also come into play once you get into breeding.
There are three basic distance types on FFH: Sprinter, Miler, and Router. Genetically, this is determined from two types of genes: Speed and Stamina. Think of the speed gene as raw speed and the stamina genes as staying power. A horse with all speed and no stamina is going to run well in short, quick bursts. A horse with all stamina and no speed is going to run better in a longer race. Distance type does not IN ANY WAY influence the style your horse likes to run or the pace they prefer. Those are entirely reflective of stats.
Sprint: Sprint races are classified as races between 4 and 6 furlongs. You may run across some sprinters who have varied distance ranges (4-7, 5-7, etc), but this is the standard and most commonly seen. Two year olds will only have races available in the 4-7 furlong range, so it may be a good idea to train them in this range at first. They can be retrained once they turn three.
Mile: Mile races are classified as races between 7 and 9 furlongs. 8 furlongs equals a mile, which is how this distance type gets it's name. Horses who are milers typically have a balanced mixture of speed and stamina. Most 3 year olds will still do fairly well at mile-range races, even if they may mature to run best in routes.
Route: Route races are classified as races between 10 and 12 furlongs. You may also have heard this races called "classic" distances, which stems from races such as the Breeders' Cup Classic. These are the longest races on FFH, which in mile terms would be 1 1/4 to 1 1/2 miles. Route races are not available for 3 year olds, so these are primarily for mature horses.