Difference between "no" and "not"
Although native speakers have no difficulty in identifying the difference between "no" and "not" it can be surprisingly difficult to express.
The basic difference
However the determiner "no" cannot co-occur with other determiners such as "the", "a" "any" etc and when these are present then the negation must be made with the adverb "not".
A list of specific cases follow.
"Not" is an adverb which negates the verb and is used with
- modal verbs and auxiliary verbs (especially as contractions) to negate their action or meaning - I don't like coffee, I won't go.
- adjectives - She is not ugly.
- adverbs - She's not very happy.
- gerunds where the action itself is negated. Thank you for not smoking.
- proper nouns - I am not John Smith.
- Determiners like "much", "any" and "enough" - There isn't much water. "There isn't any blue paint."
- nouns preceded by an article “a” or “the” - I am not a judge." "This is not the answer.
- in response to yes/no questions - Can you fly? No, I can't.
- with nouns without articles - There is no water. I'm no judge. That's no answer. No way!
- with nouns preceded by adjectives - "There is no water" There is no blue paint.
- with comparative adjectives - He ran no faster this year.
- when giving prohibitions with gerunds (..ing) - No smoking.
When you are denying that a particular word is correct then any word could potentially follow "not".
- "The answer is not "running." or more colloquially - "not "running"!"
- "The word you are looking for is not "judge"."
While the quotation marks make the situation clear in written English, only context and pronunciation make it clear in the spoken language.