Mrs is the abbreviation for Mistress and is usually used, in
written and spoken English, to describe a married woman ie Mrs
Smith is the wife of Mr Smith. It can be used when talking or
writing to a married woman or about her eg "Good Morning, Mrs
Smith" or "Have you heard about Mrs Jones?" or (in a written
letter) "Dear Mrs Smith" Madam is the female equivalent of Sir and
is used when talking to a married woman whose name you do not know.
eg "Good Morning, Madam" or "Excuse me, Madam"