In all the configurations common collector, common base and common emitter, is the base always the input?
The base node is - obviously - ONE single node only.
However, a voltage is defined as the difference in potential BETWEEN TWO nodes. As a consequence - and according to the working principle of the BJT - the voltage between the base node and the emitter is the input for ALL three configurations.
However, one of these nodes is grounded (ac wise) and , thus, defines the three basic configurations.
EDIT (Comment): (Regarding the comment from Spehro Pefhany)
Also in common-base configuration, it is the base-emitter voltage that controls the collector current Ic.That means: When the base is grounded, it is the emitter voltage referenced to ground.
(After changing the PC machine a new account was automatically created and I am not yet allowed to write a "comment".)
Obviously (?) not for common base. Because it's common.
Input is to the emitter, which give you the potential of voltage gain, not current gain. Image from Wikipedia.