Here are the three different kinds of apologies. Each one has its own unique feel and purpose.
If I offended [or, hurt, insulted, harmed] you, I apologize.
The first type of apology is the most insincere, but it is still an apology. It is the kind of apology issued by people [think politicians] who do not wish to lose face, while appearing to be humble and contrite. Notice the first word, IF. The offender does not deny the possibility an offense has occurred, but also does not take ownership of their actions. In cases of this kind of apology, full responsibility is not owned by the offender.
Other variations of this type of apology:
It seems you were hurt, I apologize…
I’m not sure what I did, but I’m sorry…
I apologize you were offended [hurt, insulted, etc.].
This second type of apology is more sincere because the offender accepts responsibility for their actions and the effects those actions had. The offender is placing themselves in a lower position of power by accepting this responsibility. This apology gives the offended person a sense of respect or dignity that their feelings matter.
Other variations of this type of apology:
I see what I did was wrong, I’m sorry…
What I did was out of line, I’m sorry…
I'm sorry for _____, please forgive me.
The final type of apology is the most sincere and contains the seed of reconciliation. Here the person apologizing does not explain away or minimize their actions. This person, accepts responsibility for their actions and is showing genuine remorse or sorrow. Notice one important element of this expression of regret: the person is asking for forgiveness. By doing this, they are placing themselves in a position of humility and giving the other person the power to forgive them. But, remember this: the subtle difference between apology #1 and apology #2 is the not words or tone; it is the position of the hearts of both parties. If one party is asking for forgiveness and the other party is willing to give it, then reconciliation can be achieved.
What type of apology you offer depends on the what result you want:
For more information about what forgiveness is, what forgiveness is not and how to forgive, pick up a copy of my new book: It Was A Beautiful Day When My Father Died, available through Apple Books.