Yes. As long as they are the same length, any Ranger beds from 1983-2011 will physically interchange. From 93-2011 they'll bolt up and actually look right. The late trucks (10-11?) have a few extra bed bolts, but that won't be a concern for your earlier truck or the bed in question, and they'll still interchange.
You will need the correct taillights to fit the step side bed, they are different between the styleside, flareside, and Mazda/STX beds. You may have to do some wiring changes on the rear to make the tails and turn signals work right, but I don;t know how they were combined over the years and can't say for certain.