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A voltage follower is just a circuit where the input voltage is equal to the output voltage. It is also called a buffer and is used to produce the same voltage, but with larger current capability and lower output impedance.
I don't think there is such a thing as a current follower. A current mirror maybe. It's just a current source that has an output equal to the current being measured somewhere else.
Knowing that an ideal voltage follower has unity gain, infinite input impedance, and zero output impedance, then a current follower should have unity (current) gain, zero input impedance, and infinite output impedance. Just as an common collector stage (emitter follower) is the single-transistor approximation of a voltage follower, a common-base stage is the single-transistor approximation of a current follower.
An op amp with unity feedback is, of course, a very good approximation of a voltage follower. The only IC I am familiar with that is close to a current follower is the LM13700, which is a really cool part for an analog geek like me.
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