I'm glad in this case that there are different words for essentially the same thing. Extrude is the name used in Part, Pad is the name in PartDesign.
Part objects can consist of several not connected solids, while in PartDesign we have at most one.
In the old days of 0.16 Part and Part design could be deliberately mixed. This concept was abandoned for several reasons which I may not know all or: preparation for assemblies by providing local coordiante systems or mapping sketches not only to faces are some of them.
Alas, there are several places where not everything is available in PartDesign (Helix, faces, ...) or the handling is still very clumsy (e.g. adding features to patterns).
FreeCAD is very well usable, but is still work in progress.