In the case of the CMD DV-1, I think the DVS-based means it’s designed with users of digital vinyl systems in mind. As the Behringer page says, the controller provides control over effects units, controls the DJ might not otherwise have.
I think Behringer is using trigger-based meaning that the control is designed with the idea of triggering clips (based on the statement that the control is designed to be used to trigger clips, such as one does when playing from an application such as Ableton Live).
The pad-based doesn’t seem as clear to me. The control actually does pretty much what the trigger-based one does, it’s just designed with things like the Traktor Pro Remix Decks in mind rather than things like Ableton Live. The pads in question are the buttons and perhaps the word pad is being used because they’re more like the pads one finds on drum machines and drum controllers, but without the velocity control those devices have.