The hitch with the big flat plate is a standard 5th wheel hitch and what virtually all 5th wheel trailers are factory built to use.
The ball in the bed is for using a gooseneck type hitch. Common on stock trailers and construction trailers. You can buy a gooseneck adapter to convert a 5er to use that type hitch but some manufacturers will void your warranty if you do.
Some people use sliding 5th wheel hitches to prevent the trailer from hitting the cab on tight back in turns.
Trailers have total weights and hitch weights to consider. Trucks have tow weight ratings and payload weight ratings. The truck numbers should equal or, preferably, exceed the trailer numbers.