The word "triangle" is ambiguous when it is unclear on whether it is denoting the shape, the musical instrument or the drafting tool. The word "triangle" is vague when it is referencing the shape because it is indefinite about whether it denotes a scalene, isosceles, obtuse, right, acute or equilateral triangle.
Ambiguous words have more than one meaning, for example: the word "light" meaning "not heavy" and the word "light" meaning "not dark."
Vague words have more than one sense of the same meaning, for example: the word "child" is defined as "a young person" and that young person could be either male or female.
A test to help determine a word's ambiguity status is whether or not the word has two unrelated antonyms, for example: the word "hard" is ambiguous because it has the antonyms "soft" and "easy."