Do the functions I can use in WeDJ for iPhone differ depending on the connected controller?

Yes.
For details, visit the SOFTWARE INFORMATION on the support page for each controller.

DDJ-200
https://www.pioneerdj.com/en/support/software-information/controller/ddj-200/#wedj-for-android
DDJ-WeGO4/DDJ-WeGO3
https://www.pioneerdj.com/en/support/software-information/controller/ddj-wego4/#wedj