Christianity Today has an interesting article on languages of apology (and forgiveness). There are a number of helpful thoughts in this piece that can be helpful. The author, Gary Chapman (The Love Languages of God, The Five Love Languages: How to Express Heartfelt Commitment to Your Mate) relates this to couples, in which I think it has the most use, but it would apply in other contexts as well.
I think there is a danger of one using specific language in apology to avoid apologizing at all. The political apology (if I happen to have done anything wrong, I apologize) in which no wrongdoing is admitted, or the apology for another’s weakness (I’m sorry you’re so thin skinned as to be hurt by what I said) are generally not languages of apology, but rather languages by which one avoids apology.
At the same time, understanding that not everyone means the same thing by the same words will be helpful in building communication. It’s worth looking at.