"No" is the word used to reply to a question. It is the opposite of "yes".
Person A. "Do you speak Portuguese? Yes or no?"
Person B. "No. I'm sorry."
'Not" is the word used to make verbs negative. Example:
"I like languages" versus "I do NOT like languages".
"I do my homework" versus "I do NOT do my homework".
These are the two main differences but there are also other contexts in which they are used. Here is a webpage that will help you.