An easy way of explaining the difference would be using a tap/faucet/valve. FET has a valve (gate) that can control the flow of water (drain current) by turning the valve (changing the gate voltage). BJT has a specialized valve (base) that can control the flow of water (collector current) by having a flow of water (base current) on the valve itself. Higher the flow of water on the valve (base current), higher is the water (collector current) through the tap.
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