A Trailer Ball attaches to a ballmount, which is held in place by a pin, inside a hitch receiver tube. The trailer coupler mounts and locks on top of the trailer ball and secures itsef in place by locking it in with the coupler's latch.

Trailer balls are intended for light commercial or recreational towing  and come in a variety of sizes:

 - 1-7/8" or 2" or 2-5/16" and all come in varying capacities.

A Trailer Ball and Ballmount should be rated the same capacity, or better yet they should both be rated to the same capacity of your trailer hitch and what you will be towing because you will only be able to tow the lesser rating of the hitch, ballmount, ball, trailer coupler, trailer and vehicle.

Pintle Hitch is a type of tow hitch that uses a tow ring configuration to secure to a hook or a ball combination. Pintle hitches are commonly used on military, construction, industrial and agricultural equipment. A Pintle Mounting Plate and Pintle Hook and Pintle lunette ring need to be purchased to complete the set up. 

Pintle combos are also  commonly purchased when you need a complete setup, rather than buying the individual components seperately.

Pintle Mounting Plates

Pintle Hooks

Pintle Lunette Rings