Hi Jini. Great question, I totally understand your confusion here.
“Not to mention” is used when you’re listing something or someone’s attributes, and you want to add an extra attribute to the list. Often the thing you’re adding is the most important, or you want to stress is for some reason. Example:
"I love using iTalki to learn English. It’s easy to use and inexpensive, not to mention how great the teachers are!”
Please notice how “not to mention” introduces a NEW attribute here.
“Not to say” can also be used when describing something or someone. However, it is NOT used to add a NEW attribute to a list, but rather to MODIFY an attribute you’ve already used to make it stronger or stress your point even more. Example:
“I think he was acting impolite, not to say damn right rude!”
Notice how “impolite” and “rude” are the same attribute, but “rude” is the more forceful or critical version. “Not to say” introduces a more extreme version of the same attribute. Another example:
“She was being kind of silly, not to say totally childish!”
I hope this helps!! 😀👌