Difference Between WolframLang, Mathematica, WolframEngine, WolframScript

Wolfram Language

is the programing language.

Wolfram Engine

is the engine that reads WolframLang source code and produce output. You can think of it as the compiler and run-time environment for WolframLang.

WolframScript

is a command line interface app to Wolfram Engine. You run WolframScript in terminal, like bash python ruby etc. You type WolframLang input and it prints textual output, interactively. WolframScript is bundled with Wolfram Engine and Wolfram Desktop.

Wolfram Notebook

(or Mathematica Notebook) is a Graphical User Interface app to WolframEngine. It can display typeset math, 3D graphics with real-time rotation, play sound, and other interactive features. You get the Notebook from buying Mathematica or Wolfram Desktop.

Wolfram Player

is a free app to display Wolfram Notebook files.

Mathematica and Wolfram Desktop

They are basically WolframEngine + Notebook app. Also, WolframScript is included. (They come in versions for desktop/laptop computer, cloud/internet, or phone.)