Doug,
In my book a tyre is a removable rubber? device used on a wheel and a tire is (generally ) a non-removable addition to a wheel such as a band shrink-fitted to a railway wheel.
But there again I am British and some words have different meanings - whoever thought the Americans would have an elephant on the back (generally) of their cars, a criminal at the other end and run them on gas which is really a liquid! (OK, OK even real gas - propane - is a liquid when in the tank). Can be soooo confusing, especially when they are supposed to speaking using the English language!!!!
So never mind the odd spelling, the words are often hard enough to decipher!
Regards, RAB