Do you agree? No, thanks / No, thank you (With a comma means "No, I don't want to go, but thanks anyway.")-- Or would you omit the comma in these two when the meaning is "no, but thanks anyway"? No thanks. (Without a comma means "no gratitude." E.g., I received no thanks [or thank-you] for all my hard work.
Both are usable for saying "no but thanks anyway" however "no, thanks" comes off as much more forceful and possibly sarcastic.
I wouldn't see "No, thanks" as either forceful or sarcastic unless the tone indicates it. But in writing, I would use the comma for the polite refusal, and no comma for meaning "I got no thanks".
Well, unless you've just been asked the question, "Did you get a yes or a no?" Then it would be, "I got no, thanks."
