This is actually a fantastic question which took me a long time to figure out myself.

It is not currently possible to generate a standalone executable of Wolfram Language (WL) programs. WL programs rely on the 'Wolfram Engine' -a a 3.3GB program which executes WL code. You can write a WL program and execute it on any computer that has the Wolfram Engine installed, but you cannot run that program without the engine.

Mathematica (AKA Wolfram Desktop) is a graphical environment for writing and running WL code within notebooks. Notebooks include nice interactive GUI functionality, allowing you to quickly visualize graphics generated by WL code. Mathematica/Wolfram Desktop contains a copy of the Wolfram Engine which it needs to run WL code.

Wolfram Player also contains the Wolfram Engine, but only has a limited GUI environment for running WL code within notebooks.

Wolfram Alpha is an online-only service which can answer questions asked in natural language. Wolfram Alpha is a program mostly written using WL code, but it is running on the company's servers and cannot be downloaded.

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A limited subset of the Wolfram Language can, however, be compiled into a standalone "C" library and loaded into another program written in a language which supports linking to C libraries and can be compiled into a standalone executable (e.g. a go program or a rust program).