What's the difference between Adapter, Charger, Brick & Plug?

Apple uses the term "power adapter" for the device you use to charge your Mac -- see: Identify your Mac power adapter - Apple Support

Charger, brick, plug are terms often used by others to mean the same thing.

To add a bit to FoxFifth's reply, Apple devices (Macs, iPhones, iPads, etc.) have a built-in chip on their respective logic boards that control charging that device ... so, in theory, the Apple "charger" is considered built-in. These chips work in-conjunction with the Apple charging cable, which themselves, have several "smart" chips, and the Apple power adapter which provides the actual power.

This power adapter has also been referred to as:

• A "charger"
• A "brick" or "power brick"
• A "power supply"

As mentioned, the charging cable has two smart chips:

• One, the E75 chip, is like a nightclub bouncer. It checks to make sure that your Apple device knows that this cable is a genuine Apple MFi-certified charging cable. If you ever see a "Accessory not supported" message, most likely it is either missing this chip or is using a "knock-off" version ... typical of cheap cables.
• The other one, the NXP30, works as a voltage regulator, preventing over-voltage situations ... up to a point.