Here's the way I like to explain it. There are really 4 different easy gaits. Many breed organizations think that their breed's gait is unique, but in fact they are giving different names to the same thing.
Following is the most common name of each gait, a description and the most common synonyms given to it.
Foxtrot (marcha batida): Diagonal gait with uneven footfalls.
Running walk (passo Illano, marcha di centro): Literally a fast walk.
Rack (saddle rack, singlefoot, paso fino, paso corto, paso largo, tolt, marcha picada): The horse lifts both legs on one side together but sets the hind foot down first, creating 4 even beats. There is a slight difference in footfall timing depending on speed, but only some people recognize the difference.
Step pace (soberandando, broken pace, amble): The horse lifts both legs on one side together and sets them down close together, creating 4 uneven beats. This gait is considered undesirable in most breeds because it puts strain on the horse and is sometimes less comfortable for the rider.
There is no guarantee that a certain breed will always perform the gait it was bred for. The only way to be sure what a horse is doing is by watching a video of it.