Is a sin only counted if a person does that action or speaks about it?

Assalamualaikum, I actually wanted to know that is a sin only counted when a person does that sinful action or speaks about it or you can still be accountable for what happens in your mind? I rade a hadith which said you are not accountable for whatever crosses your mind so does this mean even if a person intentionally thinks of a sin in his mind but doesn't do it, will it still be not counted as a sin?