Schraubenkopfantrieb is a 'screw drive' or the holes and grooves on the screw head where a driver is attached and to which you apply torque. 'Antrieb/drive' in this case refers to a specific shape (myriad of forms like cross, haxagonal, lobular, square, pentagon). Both Schraubenkopfantrieb and screw drive are generic terms that apply to all screw types. You already cited the list of screw drives above.

Here's a company referring to a 'drive system' (i.e. the shape of the head, the geometry of the grooves):

http://www.acument.com/licensing/licensed-products/torx-driv...

This allows you to think of 'drive' as a system of shapes and geometries.

Innenschlüsselangriff = internal driving feature. 'Internal' because the hole/groove/shape/feature is inside the socket (female) (as opposed to external/male). 'Schlüssel' in this case is synonymous to a driver (key). An "Innensechskantschlüssel" for example is a hex "key".

Angriff/driving feature in this case (as above) is a system of shapes, contours, grooves. Once again this refers to the geometry of the screw head, the shape of the groove, etc.

Here's a great reference:
https://www.nbk1560.com/~/media/PDF/en/technical/020_Hexalob...

Mitnahmeprofil (third time) also refers to the shape of the groove. "Mitnahme" helps you understand the concept because as you drive a screw and apply torque, you take the screw with you as it were (nimmt die Schraube mit). It is the geometry of the groove that provides grip and allows turning. This is a generic term. The Wiki article for Innensechkant, for example, begins with "Innensechskant ist ein Mitnahmeprofil für Schrauben".

So in all three cases (Angriff, Antrieb, Profil), what is being referred to is the geometry of the screw head and the shape of the grooves. The difference lies solely in usage (ISO definition) and engineering practice (usage becomes solidified if engineers repeatedly use one term over another).

Hope that helps.