The terms were used quite loosely, as per the sort of definition you might be taught at junior school.
Therefore anything that you would call a plant in everyday speech would be classed as 'vegetable'. Hence Venus Fly Trap is vegetable but not one you would eat. Unless it was trying to eat you...
I thought the concept was thought up by the BBC but having just checked, it seems that this was previously a 'parlour' game in the US.
I think I was thinking about quail..