At its very basic level an apology requires the fulfillment of two parts*:
“I’m sorry I borrowed your jacket without asking” – expresses both regret and responsibility (assumes heartfelt)
"I'm sorry that you're upset about me borrowing your jacket without asking.” - Expresses regret not for an action, but for someone else's emotion – does not take responsibility.
“I’m sorry if I borrowed your jacket without asking.” - expresses regret only if a condition is true, but is structured to weasel out of any admission that it is true.
Our newest Felon, P. David Romei, was required by the judge to apologize to the Arts Council and College Station for his actions in the local paper, The Eagle. His one quarter page ad contained the following small print “apology” surrounded by a sea of white news print.
"Scripture reveals that it is far better to give than to receive. Thus, I give you my humble apology for any act of omission or commission for which I am responsible."
I’ll let you the reader decide for yourself if this is indeed an apology.
"Mom says I have to apologize to you... so sorry!"