How about "I'm sorry about that" or "I'm sorry I did that" (or some such construction admitting personal fault), versus "I'm so so sorry" or "I'm sorry to hear that, that must be terrible" (or a construction expressing sympathy)?

Also, I think "I apologize", as opposed to "I'm sorry", pretty much expresses the first without the second.

Huhuhuhhuuhuh "lacuna".