I don't know the context of what was being said to you in chat, so this may not reflect what you heard. I can just say what I understand the difference to be.
When a boy is abused there is a lot more harm being done to him than just the physical acts. He is at an age when he is beginning to build up the ideas and values that will determine how he will later think and act concerning many things, including sex. Abuse wrecks that process of building; it's destroyed for him and instead he learns all kinds of false lessons. For example, he "learns" that he is just a thing that can be used to pleasure an adult whenever the adult wants; what the boy wants, how he feels, and what he needs don't count. He loses his sense of value and worth as a person. He thinks that unwanted sex is his rightful punishment for being so worthless. And so on.
As the boy goes through puberty and awakens sexually, what good foundations does he have available to him? What values can he refer back to as he decides what he wants and how he will relate to other people sexually? Whatever he does have has been damaged or destroyed by abuse. He may not have a good sense of boundaries, for example, or he may think that sex is about using others rather than sharing something very special. I guess there must be a million possibilities, but if we all look at ourselves here on MS, I think we would all agree that in some way or another our thinking about sex has been badly damaged by abuse.
The problem is that this hurt boy is now a man and has to make adult decisions about sex. One outcome can be positive. If he gets the help he needs, faces his problems honestly and works on them, then he can, to use your phrase, "reclaim himself sexually". I take that to mean that the guy is learning to keep good boundaries with other people and enter into sexual relationships that are good for him and for his partner. He behaves responsibly and with consideration for the feelings and needs of the other person. It's an act of "reclaiming" because he is recovering something that he lost or never had: the good foundations that would have been build up slowly and solidly if he had not been abused.
But what if this man doesn't or cannot get the help he needs, or doesn't face his issues? In that case his sexual behavior will be "acting out". That is, his sexual behavior will "act out', almost like in a theater, all the false and harmful ideas he learned as an abused boy.
I can give you an example from my own past. When I was 15 my father's friend offered me a job painting the interior of a house for him. The abuse had only ended one year earlier for me, and my reaction to his offer exactly reflected the bad and false things abuse had taught me. First, I thought I was worthless, so it never entered my head that maybe I was getting this offer because I was a good painter already at the age of 15. Second, I had "learned" that generosity and kindness from adults are just part of a sexual trap, so I immediately figured that this man wanted me for sex. I thought okay, I would go to the house and that's where we would do it. Third, I didn't care. I thought I didn't deserve to be treated better than this, and I thought what the hell, at least this time I will get paid. So when I accepted his offer and went to the house on the day we agreed, I was "acting out"; I was behaving sexually on the basis of what abuse had taught me. Fortunately for me, though, this was a good man; I got to the house and it was full of paint cans!
There are of course many other examples. A young man who was abused as a boy can easily fall into the trap of prostitution, not because he is bad, but because being used sexually is what he knows, and because he has lost his sense of his own value, or because he doesn't see that now as an adult he has a choice. Or a guy may get deep into pornography, not because he really likes it; in fact he may hate it and feel ashamed of looking at it. But as an abused boy perhaps he coped by closing down emotionally and refusing to "feel" anything. Now he's a man, and that same inability or refusal to feel may still be with him, so he needs the extremes of staged porn in order to gain sexual satisfaction. Or a man who is absolutely heterosexual may feel the desire or need to give oral sex to another man, even a stranger, just because this is what he had to do as a boy. He is "acting out", as a man, what his experiences from boyhood taught him about sex.
So I would say, Visha, that "reclaiming ourselves sexually" and "acting out" are both responses to abuse. But the first is what we need to aim for, and the second is something to avoid.
In ending here, I think it's VERY important to understand that acting out doesn't happen because a man is a bad person. It happens because of the terrible things that have been done to him as a boy. There are REASONS why he is doing this. A guy who is acting out should not blame himself for this. Yes, he has to take responsibility, but taking responsibility here means facing his issues and getting the help he needs. Endlessly blaming himself is NOT the answer. Doing that just confirms the bad feelings and causes him to act out even more.
Hope this helps!
Nobody living can ever stop me
As I go walking my freedom highway.
Nobody living can make me turn back:
This land was made for you and me. (Woody Guthrie)