Simi83 is more accurate in her answer.
"none" refers to the quantity of something, the number. How many? 0, or none.
No can be used is a number of situations to express something negative like:
"No chance,or no way" , meaning it will not happen
No also can mean incorrect, not right -- it is also a common response to a question
Example: Q: Do you like coke? A: No. ; No, I do not like it.