PLC refers to automated machinery in it's use of Programmable Logic Controls. CNC refers to automated machine tools and it's Numeric Control. I most cases a PLC is used in a CNC to obtain that numeric control. CNC term is usually only used in those machines used to machine parts.
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Just add one point that wasn't covered. The first word of CNC is computerized. As ozzb indicated, there may be other ways to "control" a numerically controlled machine than using a PC now.
Another issue however is the sophistication of the control capability. CNC systems imply full machining capability, including the "gold standard" of coordinated motion control, "interpolated motion"; the coordination and simultaneous execution of complex curve machining using 3 or more axis of motion. Most PLCs are not capable of that without adding motion control modules to them. On the other hand, a CNC system is probably incapable of any kind of process control such as PID loops, which is something a PLC can do. So in essence you can place a PLC into many different control platforms, including being part of a CNC system, but a
CNC system is dedicated to a specific task even though that task may be inherently something that a PLC needs help with.
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