Single/plural

As far as meaning is concerned, "der Mensch" means "human", that's males and females of the human species. "die Person" is, just as in english, "the person" - it's a human being but person isn't as scientifically speaking, isn't it. "der Mann", that's simply "the man" - there is "die Frau" - "the woman" and "der Mann" - "the man", it's a male human being. The German "man" has nothing to do with that. You use that as a neutral word, as you do with "one" in English for example. If generally say "One should not do that!" then it's in German "Man sollte das nicht tun!"

Is there difference in the meaning between each of the three single/plural words? i.e., "der Mensch'', "die Person'' and "der Mann/Man''?