"Servo PLC" and "vector PLC" make no sense. Maybe a "servo PLC" is a PLC that is capable of being used for motion control, but I've never heard it described that way. Someone is confused.
With inverters, there are Servo DRIVES, and Vector DRIVES, and they are typically both "inverters" I suppose. A Servo Drive is the power supply for a Servo Motor. A Servo Motor is a type of Permanent Magnet AC (PMAC) synchronous motor or DC motor, either PMDC or Brushless DC (BLDC), used primarily for positioning control, characterized as having a low power-to-mass ratio and a built-in positioning feedback such as an encoder or resolver to work with the Servo Drive. A Vector Drive is strictly for AC Induction Motors, like a regular VFD (Variable Frequency Drive) except with a lot more capabilities in high precision continuous speed or torque control of the AC motor, and even some positioning capabilities approaching that of a Servo in some cases. Servo motors will stop being cost effective at somewhere around 22kW (although I've heard of up to 100kW), whereas AC induction motors go up to hundreds of thousands of HP (last I heard, +-300kHP was the largest made), although I've heard the largest Vector Drive / motor combination was "only" 135,000HP.
JRaef2, I love your explanation. One slight detail, modern vector drives are capable of running permanent magnet motors. e.g. "[PowerFlex 525] Provides permanent magnet motor control to help improve energy efficiency and reduce related costs." Quoted from http://ab.rockwellautomation.com/Drives/PowerFlex-525. I'm using Allen-Bradley as an example only because I know it off the top of my head; it's not unique to them.
Sage Automation, Inc.