No is a more definite answer than not really. Here is an example: A woman asks her boyfriend if she has gained weight. He knows she is really sensitive about it, so one would think if he didn't think she had, that he would be 100% clear and just say "No!". Instead he said, "not really". It came across as really ambivalent to her and made her feel like he thinks she has put on weight. So you can see from this example that there is a definite difference between a clear NO and "not really". How you use these 2 expressions is up to you.

"No" leaves no room for argument. It is a nice, clear, simple answer. However, depending on the situation, it can also be abrupt and even start arguments. "Not really" essentially has two meanings. Most accurately, it means "not quite no" or "almost no". Eg. Do you want to make dinner tonight? Answer: Not really, but I will anyway... Eg. Have you started your book report yet? Answer: Not really, I just chose my book... In common usage, though, it's usually a polite way of saying no. Eg. Does this outfit look good on me? Answer: no. Polite answer: not really... Eg. Do you want to order McDonald's for dinner tonight? Answer: no. Polite answer: not really... In general, if someone asks you a question and the answer is "no" and you want to avoid confrontation or a potential argument, it's better to say "not really." If you DO have a strong opinion and are comfortable stating it (or it's a trivial matter - "do you like the colour green?") then "no" is a better choice.