In english there is difference between thanks and thank you.
Is there a difference between merci and merci beaucoup ? If yes .Is it about the person's age or the extent of my knowledge of the person?
No. "Merci" means "thanks / thank you" (there's no difference in French), and "merci beaucoup" means "thank you very much". "Beaucoup" is an adverb used to express a big quantity or intensity. With "merci beaucoup", you say that you are very thankful to whom you're speaking. It doesn't depend on how well you know the person, or their age or anything, only how thankful you are.
(I think "merci beaucoup" is a bit colloquial. I wouldn't use it in a formal letter. Other expressions would fit better, e.g. "un grand merci", roughly meaning "with great thanks".)