Right, your SPS is just a version of the BDL. It used to be a lot simpler when Remington only offered ADL and BDL.
The confusion came several years ago when they decided to discontinue both ADL and BDL. ADL had always been the blind floorplate budget gun and the SPS was intended as a replacement budget gun, but with a floorplate. The BDL stock style was changed to a more classic look and designated the CDL. And then there was the DBM, with a detachable box magazine.
Both the ADL and BDL have been brought back in limited numbers and chamberings and usually only sold at big box stores such as Walmart etc.
They have also offered numerous versions of all 3, ADL, BDL, and CDL, over the years, but when ordering an aftermarket stock you only need to know 4 things.
Does it have a floorplate (BDL), blind magazine (ADL) or detachable box mag (DBM).
Barrel contour.
Short action or long action.
Left or right handed.