Rehearsal Props are the ones used for the rehearsal process. They are usually pulled from the stock of the theater and used while a production is in rehearsal. Some of them may be converted and used in the actual performance. During the first few rehearsals a Stage Manager will usually pull some Rehearsal Props from the Theater's stock of props for use in rehearsal. Whether or not any of these become permanent is up to the director
Trick Props are props that have some sort of hidden function that may not be readily apparent. The most common trick prop is a trick knife. The knife looks like an actual knife, but it is spring loaded so that when it is pressed against a harder surface it retracts into the blade. Trick Props are usually custom made or made with a specific purpose in mind. Actors should be taught how to use them properly so that they are not played with or broken
Any Theater worth it's salt will keep at least one type of fake gun on hand that fires blank bullets.