Handicap

A race where a handicapper has assigned weights to be carried by all runners on the basis of their past racing efforts.

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).

Allowance Race

A race with non-claiming conditions set by the racing secretary. They are meant to be a step down from stakes racing.