My understanding of swash plates led me to believe that the pistons in a swash plate pump rotate around with the driving shaft along with the chambers in which they aspirate (e.g. M&S Hydraulic Youtube video on swash plate plumps). As the axial position of the pistons change, the piston chambers draw and expel fluid.
However, I just watched a training video from "Our Virtual Academy" (which costs money to view unfortunately) where the pistons do not rotate with the shaft; instead, the swash plate rotates causing the pistons to move axially. The angle of the swash plate is varied by forcing pressurized fluid into the control chamber (here is an example).
I can't imagine why one would use this latter form of swash plate pump. What are the reasons for the different approaches? (What is the correct terminology to distinguish the two so I can carry on my own research)