Trifecta
A wager picking the first three finishers in exact order. Called a "triactor" in Canada and a "triple" in some parts of the U.S.  

Trifecta Box
A trifecta wager in which all possible combinations using a given number of horses are bet upon.  

Trip
An individual horse's race, with specific reference to the difficulty (or lack of difficulty) the horse had during competition, e.g., whether the horse was repeatedly blocked or had an unobstructed run.