Do you show

1) Thai passport

2) US passport

3) Both passports

?

Normally you show both at check-in so they can check that no visa is required.

At immigration you leave Thailand with the Thai passport, enter the US with the US passport, at check-in show again both passport and leave the US with the US passport and enter Thailand with the Thai passport.

Depends on what passport you used to enter. If US passport that is all that has to be shown. If entry on Thai passport you must exit on that also and the US passport would be shown to desk to prove you do not need a visa.

I took my son and wife to the states a few months ago. We did show both of my sons' passports in BKK. if my memory serves me right this is how it went:

He entered the US on his US passport.(no reason to show Thai passport) and departed the US on his US passport. he reentered Thailand on his Thai passport.