Scratch

A horse is a scratch when injury or other necessity causes it to be withdrawn from the race.

Pari-Mutuel

A pool style wagering system, where all money input through betting is divided among those with winning tickets (save for various deductions by the track operators).

Exacta

A bet selecting the first and second horses in a race in the correct order. An exacta box refers to paying a little more to ensure they can finish in either order.