If you go out to the farm and see a big red tractor that turns on and can pull a trailer around the field, then it is a functional tractor (in the first definition). If you go to a farm and you see a station wagon pulling a hitched-up trailer around the field, then it's a function tractor (in that it isn't actually a tractor, but it functions in all the same ways that a tractor does).
This second definition I find endlessly fascinating. It's like saying "if it walks like a duck and talks like a duck, then it is functionally a duck." It doesn't matter if it's a duck or a man in a duck suit or a fox in a zebra suit; when it covers all the factors that are relevant to determining duckness, then it doesn't matter what things make it not a duck; for all intents and putposes, it's a duck.