Across the Board

Refers to betting on a horse to finish first, second, and third to cover any of those scenarios happening during a race

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.

State-Bred

A horse bred in a particular state and thus eligible to race in restricted state-bred races. These can be anything from maiden races to stakes events.