A microcontroller is an integrated circuit, essential a microprocessor with extra input/output and memory built into it. To use it it needs to be built into a circuit and have software written to make it do anything.
A PLC is is a self contained unit which probably contains a microcontroller, but has a user interface and connections for inputs and outputs..it can be programmed by the user to react to the inputs and drive the outputs.
A CNC machine is a machine which can be programmed by the user.
I'm sure someone will want to elaborate on this.
(I reserve the right to be of no help what so ever )
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