If you call your API REST, some zealots will open up your API and look if your beautiful response is polluted with any "links". If it is instead pristine, they will claim your API is not REST.
It's really ridiculous, the links system is only barely useful in some GUI data exploration tools, that are not even that comfortable to use.
If you use a JSON API that feels weirdly antiquated because of the superfluous fields, this is why. If you disregard HATEOAS basically every JSON API on the web is REST.
So almost any site you hit with your browser is a "RESTful API". Another decent example is Atom Syndication / Atom Publishing.
The best introduction that I've found is Jim Webber's 2011 talk https://www.youtube.com/watch?v=aQVSzMV8DWc&t=3m8s Jon Moore's 2010 Hypermedia APIs talk is also good https://vimeo.com/20781278
Unfortunately, a second idea appeared, that embraced the label "REST" but used it to mean something else (roughly, a set of conventions for how to organize web pages and the edits one makes to web pages). And the second idea was written and shared with a much larger audience than the first (in addition to being an "easier" idea), so it grabbed a super majority of the mind share.
I said something to that effect in a job interview once when the topic of REST came up. I was looked at like I had two heads.
https://engineering.3ap.ch/post/using-hateoas-with-rest/
I think the main distinction according to the original paper is if you are doing just HTTP CRUD ( not REST) or also HATEOAS