IMO it's never as black and white as that, and you will always find people who have been in each situation, so the one who forgave their partner only for that partner to go on to cheat again, but then you will find someone whose partner cheated, showed remorse, they went to couples therapy, worked on the issues which led to the affair, and their relationship lasts. And conversely you will find people who had an affair, left their marriage and are happy elsewhere but would never do it again, while there will be those who leave the marriage and then go on to cheat again when the new relationship becomes monotonous - iyswim.
From my own experience the one thing which is crucial to recovering from an affair is complete honesty on both sides. That doesn't mean that the betrayed-upon partner needs to accept any of the blame, affairs are not justified, but it's simplistic to suggest that there is never a catalyst which leads to an affair. But if what the cheater says is the reason isn't something which the cheated-on can identify with, then chances are the relationship won't recover. So e.g. if the cheater says there was no sex and the cheated-on knows they've been doing it three times a week then the cheated-on isn't going to feel they need to have sex more to be a part of fixing the relationship and neither should they. however, if there's been no sex for two years and a refusal to engage on the matter, then it may be possible to work on those issues in order to repair the relationship. That being said, the person being cheated on may just feel that the relationship can't be repaired and may choose to end it anyway, iyswim.
I was cheated on but then ended up cheating in the same relationship. My ex had an affair just months after we moved in together. He denied the affair but admitted the infatuation with someone else, his justification was that he felt we were possibly different people, he didn't like the music I listened to or the clothes I wore, and yes, the reasons were that simplistic. We moved past it and I made efforts to change. Meanwhile the ow ended their affair because she sstarted seeing someone else who was married. ex never showed any remorse, just justified his position. What I didn't realise was that this was in fact the beginning of an abusive relationship. Over the next fifteen years or so he completely broke down my confidence, isolated me from people, convinced me that I had no real friends, moved me away from any support network while dc were still relatively young, and then isolated me further. He made it difficult for me to go back to work, thus meaning I was financially dependent on him. Over the years we talked about splitting up on numerous occasions. Something would happen and I would withdraw and talk about splitting. But then something would always come up which made it impossible for me to make that ultimate decision. And then I met someone else who made me see that there was more to me than who I had become. And I'm afraid to say that I had a brief affair. I didn't leave for the OM fwiw, but that affair made me realise that I could never stay where I was. I do however bitterly regret the way in which I had ended my relationship, and wish I'd had the courage to do it sooner. And I can honestly say hand on heart that I would never, ever have another affair. My ex would have forgiven me, and wanted us to try again. But I knew that life would have been even more unbearable if that had happened, and I realised that I didn't love him. A part of me felt that I should try again because I owed it to him to repair the hurt I had caused, but I couldn't do it, so we split nearly four years ago. The reason for the end of the relationship was my affair, I am therefore considered 100% to blame and will carry that for the rest of my life. but there were so many things which led up to a point where I had an affair that it really is never that simple. that doesn't justify the affair, affairs aren't justified, but it just never is as simple as someone wanting some fun elsewhere. If your self esteem is at a point where you believe you are worthless and someone tells you that's not true, then you can find yourself vulnerable. The key is to recognising the boundaries and never crossing them, if someone has done that once then they know the next time what the boundaries are.
What I would say though is that there is no right or wrong answer wrt the reaction of the person who is cheated on. Some people want to try again, and at that time that action might be right for them. It may work out, it may not, but while it's often easy to give advice based on experience, every person and every relationship is different. So if the op's friend feels she wants to work things out then that may be what she needs to try in order to bring her to the place where she realises it's hopeless, or it may in fact work for her and they may resolve any issues, he may be remorseful, and the marriage may last for another who knows how long. similarly an affair might be an immediate deal-breaker, and equally that is what someone should do if that's what they feel, and no-one should feel pressured to stay with someone just because that someone says they're sorry and want to try again.