Usually there is only one derailleur hanger that will fit your bike frame, however with Shimano’s direct mount derailleur they have introduced the possibility of a second, longer type which attaches to Shimanos direct mount derailleurs (SRAM don’t have these as yet). The reason for this is to eliminate one of the links in the derailleur to frame mount and strengthen this area.
As you can see in this picture, the standard mount hanger (right – Cube 149) and direct mount hanger (left – Cube 10148) have exactly the same profile where they interface with the bike frame, but have a different profile for the attachment to the derailleur:
Compatibility:
Standard mount hangers will obviously fit standard mount derailleurs (not pictured)
A) Direct mount hangers are designed to fit direct mount derailleurs
B) Standard mount hangers ARE backwards compatible with direct mount derailleurs, but ONLY if you use the additional b-link, and obviously you’re adding an additional link in so you’re not getting the benefit of the direct mount derailluer
C) Standard mount hangers are not compatible with direct mount derailleurs WITHOUT the b-link
D) Direct mount hangers are not compatible with direct mount derailleurs WITH the b-link
Long cage vs short cage derailleurs
To complicate matters further, derailleurs also come in short or long cage versions, in summary for 2x or 3x front ring setups, you’ll need a longer cage to accommodate the slack from the extra chain needed. This doesn’t really have any bearing on the hanger setup though!