"Ambiguous" could mean a few specific things, but vague could mean anything. Examples: She told him she really liked him, but he found this ambiguous: did she mean as a friend, or was she expressing romantic interest? These instructions are really vague: I don't know what I should do!

When something is said or expressed or written in a way, that is unclear, not fully explained and difficult to understand, it is then a vague expression or statement. When something is said or expressed in a way that could have several interpretations and could be understood in more than one way,which could be contradictory as well,then that is when the speech or expression is 'ambiguous'.

ambiguous = double meaning vague = unclear meaning Usage should be obvious.