The 500 has a magazine with a closed end. The barrel fastens to the end of the magazine tube with a thumb nut.
The 590 has an open ended magazine tube and the barrel is held in place with an end cap. The 20" barrel of the 590 usually has a bayonet lug. (Whoopie)
The receivers are pretty much the same.
There was a 500MIL or USA model that was actually a 590. It gets confusing sometimes.
There are numerous variations of both models. Various finishes and barrel lengths. Take a look at the Mossberg website for more info.