"No, thanks" with a comma, I think, means, "No, but thank you, anyway."

"No thanks" without a comma means "No gratitude; I didn't even receive a thank you."

I believe the same would apply to:

No, thank you. = No, but thanks anyway.
Example - "Would you like another piece of cake?
"No, thanks" OR "No, thank you." Good to both?

No thank you. = I didn't receive as much as a simple thank you for what I did to help him. Good?

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Comments  (Page 2) 
Very few people worry about a comma in spoken language use. If you’re using some form of written language use to ask those things then, contextually, the use of lack of use of comma is likely to be enough to do the work the comma would otherwise do. In short, your logic is sound but Pragmatically it’s usually superfluous (the comma, and the logic used here), from a descriptive linguistics point of view.

No; I never made a request for anything.

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