Not all 870's will have threading for chokes. Some are meant for slugs and buckshot, and so those aren't normally seen with the threads to accept a choke. It's best to ask for the specific exact model and barrel, or ask the counter clerk. Or, get the seller to take a pic of the muzzle!
"Rem Choke" refers to the removable chokes that fit in Remington shotguns. "Modified" indicates how much restriction that particular choke gives your pattern. You may only own the one choke, but you could buy many more, as long as they fit "RemChoke". Examples might be Improved Cylinder, Full Choke (my favorite for Trap shooting, gives a very tight pattern: either you hit it or you didn't), Improved Modified.
Many older shotguns, for instance earlier Remington 1100's, and some Winchester Model 12's, came with the one barrel, and did not have removable choke tubes, they were fixed choke right from the factory.
Why is this done? Well, slugs are ideally shot without any choke restriction on the barrel, and can be dangerous w full chokes. With Skeet, the clays are much closer and faster, so you want a lot of spread, so maybe you choose Improved Modified (I'm not a skeet shooter so don't criticize that example please!). If you shoot some Trap, and want to do more of it, get better at it, Full Choke is what you want: it will punish you with a zero for what otherwise might be a 'lazy hit', but reward you with a clear consistent hit when your aim and lead is "on". Meaning, it makes you a better shooter with a shotgun. Other shotgun games, like Sporting Clays...well, they are faster, smaller, closer and different enough that you want to ask some experts in that game, but I'm guessing it won't be a 'full'!