there's not so much a difference, it's more that the 590 is a specific configuration on certain variables....
Mossberg 590 Special Purpose shotguns are all 20" barrel, 9-shot (or, magazine tube is flush with the barrel from the factory) shotguns.
590A1 are the same receiver as 590, metal trigger guard, metal safety switch, and the reinforced barrel wall. Available in 18.5" and 20", 6 (non-flush) and 9 (flush with 20") shot varieties.
Bayonet lug is available on both 590SP and 590A1, but only in 20" 9-shot models. Both recievers can accept the heavy reinforced barrel, if you want to switch them around. I don't believe a standard 500 will accept the heavy barrel, but I don't know.
The 500 Persuader is basically a 590SP, but it only comes in blued steel iirc, and will not accept the heavy barrel if you choose to upgrade that later. The comment about the magazine cap is the biggest difference probably, as the 590SP and 590A1 tubes are much easier to completely disassemble, whereas the 500 is blocked at the end.