In an electric circuit, voltage is controlled by current. Current is controlled by voltage. What controls what?
A BJT has an exponential (diode) response to voltage on the Base/Emitter junction. It is difficult to control any of the currents, because you have to generate a log function of the input signal to go into the exponential object to get the output you want. If you just want a switch that doesn’t matter.
The Emitter / Collector current is roughly proportional to the base current, so you can get the output you want by controlling the base current as you want.
But a FET isn’t called a voltage controlled device because it has a nice linear response. It’s called a voltage-controlled device because it requires very little current to control it. Language is funny like that sometimes.