PS3 controller also for PS4?

We bought a PS4. Because my daughter wanted to just dance, I bought a move controller and camera on ebay. That was apparently wrong because these were PS3 stuff. Because it was the PS3 Move Starter Disc too. My partner tried and couldn't. So he bought a new PS4 camera in Media Markt. Because with PS4 Just Dance you don't need a controller! All you need is the camera. Then of course it went perfectly.

But now I just see that amazon also has this Move Controller for the PS4.

https://www.amazon.de/...079JCLPBC/

What do you need them for? And would my single move controller on the PS3 be useful for something, or is it just PS4 stuff?

The normal controllers of the ps4 have the same function, can also be used as move controllers, the ones on Amazon are just easier to use e.g. For SingStar as a microphone