I've felt there are two categories of 'I'm sorry' which many people (including me!) have used:
TYPE 1: the true apology, where the apologist is genuinely interested in changing their actions and/or perspectives. They are generally willing to listen, to learn, to progress, to practice further conscientious behaviour.
TYPE 2: the false apology. We've all encountered it, online and offline. It's an apology of defense. And it's generally repetitive, because it doesn't mean anything so the mistakes keep happening. The apologist continues to think and behave in the same way they always do, with no true intention (subconscious or no) of educating themselves or becoming more understanding of another's situation. They say 'I'm sorry', but because it's false, they will return to their old patterns, make the same mistakes, apologize again.
Some people do this their whole lives without learning a thing and not caring. Others become bitter and resentful that they are 'forced' to apologize so many times for the same things. This leads to blaming the harmed person (or group) for being harmed at all. It's your fault that you took offense.
SEMI-TYPE 2: the passive-aggressive apology. It generally goes "I'm sorry that you're upset" or "It wasn't my intent" or "I'm sorry you took offense". This isn't even an apology, which is why I don't categorize it. It places all the blame or harmful action on the other person and willfully makes the semi-apologist look like a naive innocent. Again, it's another situation of 'it's your fault you were hurt by my actions'.
and a newly added third category -
TYPE 3: the insecure apology. I learned this one from my BFF/roomie, who compulsively apologizes for everything whenever she is personally in a bad headspace. (for example: she'd come home, put her bag down and say "Sorry". She'd say "Can we watch ___ tv show? I'm sorry"). I learned from her that this is an apology that stems from insecurity - she is convinced that her every action and thought makes the other person annoyed. That every opinion she has is wrong. She generally does this if she's stressed out or depressed.
Type 3 is one I had to learn to understand, because I wasn't familiar with it. I have unending sympathy and understanding for Type 3 apologies, because I know it stems from stress/insecurity. However, I did explain to my BFF that her constant apologies then put me in the involuntary role of the daily villain. She put me in a position of constantly disapproving authority - authority that I didn't want or have or encourage. I was cornered there, because then I was obliged to 'forgive' her. It was a false forgiveness, because I wasn't upset in the first place. I didn't want to be a villain, I explained this and we compromised for the better. <3 her.
Any other types of apologies that you have encountered, either online or offline?