''It doesn't concern you.'' is closer to ''It's none of your business.'' Both mean that you are not invited to be included in whatever others were talking about. ''It's not about you.'' means something completely different. It means that you made a situation/event about yourself, and others are aware and tell you this. For instance, Doctor Strange takes the situation of him saving lives and never having not saved one as something he's very proud of so much so that he doesn't treat people who are untreatable. So he only treats patients in order to raise his status as the best doctor. The whole story is to get him to learn that it's not about him, it's about saving lives of others.

They do not have the same meaning. "It's not about you" means that whatever this person is talking about does not concern "you" or is not related to you. "It's none of your business" is used to say that something is private information and should not be asked about. References: https://www.merriam-webster.com/dictionary/none%20of%20your%20business

It is possible, in some cases, that "It's none of your business" and "This (subject or conversation) has nothing to do with you!" could convey same or similar meanings. However, "It's not about you" and "It's none of your business" do not quite match here. I think, if you used "It's not about you" instead of "it's none of your business," the native english speaker might understand what you mean to say.

It would be common to hear these sentences together: "it’s not about you, and it’s none of your business."

Roughly the same, maybe a slight difference: "it's not about you" usually is about a problem in a relationship between the speaker and someone else. "It's none of your business" could be the same, or could be about a feeling the speaker has which they dont want your opinion on.