Well, if you want to really really get technical...
From the Wikipedia entry for Fuel Cell...
A fuel cell is an electrochemical cell that converts the chemical energy from a fuel into electricity through an electrochemical reaction of hydrogen-containing fuel with oxygen or another oxidizing agent. Fuel cells are different from batteries in requiring a continuous source of fuel and oxygen (usually from air) to sustain the chemical reaction, whereas in a battery the chemical energy comes from chemicals already present in the battery. Fuel cells can produce electricity continuously for as long as fuel and oxygen are supplied.
Since even Wikipedia thinks that "fuel cells are different from batteries", I don't see why you should be surprised that some girl answering the phone at Toyota
thinks they are different too.
Could a Toyota fuel cell be rigged to power a Tesla? Probably.
Could Tesla's battery system be used to power a Toyota? Probably.
But neither one is very likely to come to market.