Which version of Android is this? I see no such menu in my phone. There's only SIM storage, which should never be used except to import old contacts, phone storage which should only be used when you don't want your phone to be linked to an online address book, and synced storage which is usually Google account but other apps that are installed on the phone might also provide facility for their address book.
Phone storage, Google Contact synced storage, and Google+ synced storage provides grouping ability. Availability of grouping for third party synced storage depends on their implementation. Contacts from multiple address book providers can be joined into a single entry, so it can be used as a workaround to group contacts when the third party address book provider doesn't provide grouping facility of their own.
Yes, contact management in Android can be a bit complicated, but that's because it's trying to solve a bigger problem, which is that most people have multiple address books with overlapping contacts. For example, I have Google Contacts, Hotmail, Yahoo, Skype, and WhatsApp. The ability to manage them from a single app, and join contacts from different address book providers is just ingenious.