I use hugo a lot, I also made my own static site generator called Rubedo which is very similar in concept to hugo and other similar SSGs, but with much more of a "batteries not included" approach. The idea is that existing SSGs are nice but if you're trying to build something that is not a blog or blog-like thing it starts getting cumbersome, and that's where rubedo comes in.
I think most people here (me included) suggest hugo because it's simple very well supported, although not without its issues: the templating is a bit obtuse and again if you're trying to diverge from the "blog" archetype you're gonna need to do some trickery in my experience (I made a quite complex theme for hugo so I would know).
If you're feeling like messing around with a different approach and doing more work you can try out rubedo, maybe even open an issue or two along the way. Another thing that you might like about it is that rubedo uses Tera for templating, which is heavily inspired if not mostly identical to jinja2.
They're template engines, not languages. They use a language and different engines may have similar if not identical languages.
There are multiple engines because each engine is usually made for a specific programming language: jinja2 for python, tera for rust and idk about twig.