Corrected entry: On the show, "soda" is usually offered when asking if someone wants a drink. In Michigan we always refer to any carbonated drink as "pop". Maybe transplants might say soda, but if Tim and family have been there their whole lives, they would drink "pop".
Corrected entry: In the episode with the rope swinging at the beginning when Tim has finished rope swinging he lifts is head a little, on the overhead shot you see the stunt mans face instead of Tim Allen's.
Correction: Adding on to what Lummie wrote, people are also influenced by family members, teachers, etc. I live in the Southeast USA and my family has always said soda - even though a few surveys claim that it's common for people around here to say "Coke" (as a term for multiple brands).