The common useage (in this 'hood) is "check", and when you get it, especially at the corner "ham 'n egger" or "greasy diner", they tear a sheet out of thier pad and it says "CHECK No.(insert # here)" right at the top.

I always say "bill", or comment to a "check" request with "They pay you to eat here?".

BYB - Is there a difference between a reciprocating engine and an internal combustion engine? Isn't that the idea behind having pistons in the first place?