Beautify, format, pretty-print: one operation, three names
It is worth being straightforward about this, because the terminology causes real confusion. Beautifying JSON, formatting JSON and pretty-printing JSON are the same operation: parse the document, then write it back out with line breaks and indentation. There is no technical difference between them, and no tool anywhere produces different output for one term versus another.
The three names come from different traditions. "Pretty-print" is the oldest, borrowed from Lisp and used in `JSON.stringify`'s third parameter and in Python's `json.tool`. "Beautify" arrived from the JavaScript tooling world, where jsbeautifier and its descendants popularised the word. "Format" is what editors and language servers call it, and it is the term Prettier and the VS Code command palette use.
So if you searched for a beautifier and landed here, you are in the right place - and so would you be at the JSON Formatter. This page leans towards the readability side of the job: choosing an indentation style and knowing when indentation alone is not going to make a document readable.