Is Sparkfun's MicroView OLED Arduino module a shield? I'm getting confused by the Arduino terminologies:  shield, breakout, module.

Is this MicroView an Arduino compatible shield that will plug into Arduino's or Adafruit's Uno?
No, MicroView is not an Arduino shield, so you can't plug that into any Arduino. Arduino Uno and MicroView are developed based on Atmega328 controller. So it is 100% code compatible with Arduino Uno, means the code that runs on an Arduino Uno will also be able to run on the MicroView.