"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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only "no thanks" is enough. I did not hear "no thank you" yet.
Mister Micawber/Wordy:

Do you agree with my logic above with the commas?

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You are making a distinction that native speakers do not.

Would you like some tea? No thanks.

How about a donut? No thank you! Very kind of you though!
You kidding? I most certainly pause where the comma is... and I have been natively speaking for 31 years
No he's not. There's no aspiration between no and thanks, or no and thank you.
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LOL of course there is. "No, thank you" is the proper form. You cannot "no thank" someone unless you are a caveman maybe.
I'm a native English speaker, and it has occurred to me.
That's how I ended up on this page!
Completely agree with your logic. Most native speakers indeed do not use commas on a regular basis, which does not make the commas optional if you want your sentence flow to be smooth and readable.
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