Initially, after exposure or confession, a lot of waywards say what they think needs to be said to salvage a relationship they want.
They are sorry. Sorry they got caught, sorry they did it, sorry about the mess.
They wish they hadn't done what they did.
They recognize the consequences, at least in part.
They cry, they talk, they act like they understand what they did, and why they did it.
But, speaking from my own experience and what I've read from a lot of others, they don't really understand what they did to their partner, how awful and dire the pain is that the partner feels. They also don't really understand why they did it, they just think they do.
The true remorse starts to kick in when they gain that understanding, and they realize why they did what they did, and how horrible it is to do to someone, as well as how helpless the other person is to do anything about it at the time it is happening. To compare to something, it's like slapping an infant. The infant can't do anything about it, just feel the pain. At least at the time, the BS can't do anything about it but feel the pain, they can't control their WS.
When my wife "got it", it was 5 months into MC, she was lying, obfuscating, trying to control counseling by doing this, and desperately wanting to avoid exposure of what she actually had done. Through it all she insisted that she had come clean, that she had told everything, that "you just don't believe me" and that "I've told the truth, you just can't handle it".
Then, one day, after counseling, we were walking to the car, she was literally shaking (it had been a rather mild counseling session so this was an odd thing). When we got in the car, she sat in her seat, I asked "what's wrong".
Her reply was interesting, but a bit puzzling.
"I just realized that I treated you like someone who had rejected me."
Around 1 month later, after agonizing on what was happening, she dropped to her knees in front of me in our back yard, without any preamble, and began crying and confessing to what she had actually done...which was not what we had talked about in counseling.
Over a year later, after the hell that I went through because of this, and looking back upon this time I realized that this was when true remorse developed.
She treated me like someone who had rejected her, but I hadn't rejected her, and she realized what it had put me through.