Wolfram|Alpha and Wolfram Language are two completely different things:

Wolfram|Alpha is a natural language computational engine which takes queries and computes custom answers based on back-end knowledge databases and a large amount of Wolfram Language algorithms.

Wolfram Language is a computational (programming) language. There is a good 'fast introduction' for it here:

http://www.wolfram.com/language/fast-introduction-for-progra...

The full reference documentation for the Wolfram Language is located here:

https://reference.wolfram.com/language/

(It's extremely well-documented with extensive examples for every function).

I use my university Mathematica license rather than use WolframAlpha because I can never figure out exactly what the latter can do. Wolfram Language, in contrast, has ok enough documentation and a predictable programming model. (It's not perfect---I have a long list of complaints about its design---but it seems to be the best for the kinds of symbolic calculations I'm doing right now.)

> - It's arcane/esoteric

Even he admits to this ,

" What Kind of a Thing Is the Wolfram Language? I’ve sometimes found it a bit of a struggle to explain what the Wolfram Language really is."

https://blog.stephenwolfram.com/2019/05/what-weve-built-is-a...

But that's because he's trying to explain how amazing he is rather than actually explain the language usually.

Wolfram Engine is like command-line Mathematica.

Which means you get access to the full functionality that Mathematica offers, just without the GUI notebook interface.

See: https://www.wolfram.com/mathematica/new-in-12/