PLC - numerically controlled machine?

You could but most people think of Numerically Controlled machines as machine tools (lathes, mills, etc.) with a specific type of control system that is programmed in the everlasting G-code language. Same is true with CNC.
 
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NC was the predecessor of CNC.

Many of the early NC machines used just a single line instruction entered and executed by the operator.

The first NC machine I operated had a 10 key pad and a row of function keys, and an LED numerical display. Pressing the keys "Line X 5 Y 1 FR 10 Enter" would move 5 units +X, 1 Unit +Y at 10 Units/min. The cutting spindle already had to be on and the Z axis was set manually. Once the move was done, you had to enter the next move. There was no "program" storage.
 
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The PLC is 'dumb' = NC (I/O)
The HMI touch screen could be considered the CNC 'smart' part.

My take on it

And where does PID fit in? The NC does the internal calcs for moves, a PID does the 'same'?

I here the worms crawling out of the can, LOL

Rod (The CNC Dude)
 

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