Kevin, All Mossberg 500 series pump shotguns have same action.----------Introduced in 1960, all model 500s are based on the same basic concept designed by Carl Benson. Originally using a single action bar that was known to bind and even break, this was changed to dual action bars in 1970, following the expiration of Remington's patent on the double action bar design. A single large locking lug is used to secure the breech. The magazine tube is located below the barrel, and is screwed into the receiver. The slide release is located to the left rear of the trigger guard, and the safety is located on the upper rear of the receiver (often called a "tang safety").
It might be the biggest different factor between 500 and 590 that you should consider carefully. The magazines of model 500 are closed at the muzzle end, and it is held in place by bolting into the threaded hole at the end point of the magazine tube. However, the 590’s magazine is designed to be opened at the muzzle end. Besides, the barrels fit around the magazine tube and held on by the cap nut at the end point. Especially, the 590 magazine setups are easy to clean and remove, as removing the nut allows removal of magazine spring and followers as well.
Kevin, the 500 & 590 are the same "Action" Sir. Great details reviewed here : https://rifleshooter.com/2017/09/remington-870-v-mossberg-500-v-mossberg-590-comparative-design-notes/
They are exactly the same actions Kevin.