Is the Plutus Application Backend another name for the Plutus Playground? If not what is the Plutus Application Backend? Also is the Plutus Application Framework the Plutus Playground?
Plutus Application Backend is used to interact with smart contracts built using Plutus (Plutus Framework). Plutus Playground is a tool used to compile smart contracts built with Plutus and simulate transactions and interactions with smart contracts.
Here's a docs for Plutus tools so you can read more about them https://docs.cardano.org/plutus/Plutus-tools
Plutus Application Framework -> A collection of libraries, tools, and rules used to build Plutus apps. Think of it like a toolbox with guides/manuals, or like how Ikea furniture comes in parts and assembly instructions.
Plutus Application Backend -> A set of tools used to test and interact with the apps built with the Plutus Application Framework. Eg. It offers emulated and non-emulated access to the blockchain to determine how an app may perform in a given scenario. Imagine if a popcorn machine didn't just make the stuff but also was able to let you know how much you're making, the quality of the stuff, the bad corns in the machine, etc. You know, fancy stuff.
Plutus Playground -> A curated sandbox environment intended to mimic the blockchain, to try and experience how Plutus apps can work in a real-world/production setting. Think of it like paper trading.
Each of these three can be used independently, but they work best if combined in use.