There are thousands of types of file. They all contain data as a long sequence of numbers, and how those numbers are interpreted depends on the type of file - text characters, floating point numbers, pixel colour information or compressed data

There is only text files.

Someone will probably correct me – but the funny thing is that stuff like docx and xls are just a zipped/tarballed collection of different kinds of files. So I would add whatever the official term for “zipped/tarballed” to your list.

This is the kind of shit you'd read in a textbook from the 70s

The two types are text (encoded) and data (bytes)

Nope. Wrong. There are thousands of file types, and while a handful of them fall somehow under your four categories, most of them actually don't.

And calling .docx a "text file" is an insult to all honest text files.

I learned in computing that there are two: binary and text. If you open the file with a text editor and you can read some stuff, it's text. If just random characters, it's binary.

Not really.

For practical purposes, all files "binary", ones and zeros. And with those ones and zeros, you can encode stuff for example text and for example with ascii https://en.wikipedia.org/wiki/ASCII But you can also encode programs that can be executed, or what you named, visual, audio, or whatever you want. The differences are the "encodings".

Sometimes, things work a bit like one of those Russian Matryoshka dolls, for example a PDF can contain a JPG or a PNG but also TXT.

It's really not that simple as there being "4" types.

I'm not sure that answers your question though.

the would not look the same if you read them raw; much of a docx file is formatting and other metadata

DocX is a weird beastie, last time I researched the topic it ended up being like an XML database with a word document mask

If you have a .docx file, rename it to .zip, and extract it. You'll see the .docx is just packaged text (and image) files.

What about .exe / .dmg Files for installing programs?

Not just those. Files are just a method of storing digital data, so it's not just those four. You can have files storing databases, software (think exe, AppImage, deb, rpm, etc.), design files, projects, and more!

And file extensions are a method of telling different programs how to handle different files, since the data is formatted a bit differently. For instance, a ".txt" file is stored in plain text, while an executable file is compiled code that needs to be run.

For your example, I would like to note that you are comparing a plain text file type to a rich text file type. Plain text file types, like .txt, .md (Markdown), and the different code files (like .json, .py, .rs, etc.), can be viewed and edited with a simple Notepad-style text editor. The data is stored, as the name suggests, in plain text. In comparison, rich text file types, like .odt and .docx, encode additional data like fonts, styles, images, animations, etc., and require a rich text processor (like LibreOffice, MS Office, etc.) to read them. You can't view them through a notepad-style application, for example.

And for images, video, and audio, you have it take into account compression, codecs, that sort of thing. You might have heard that a PNG can store transparent images and is a lossless format while a JPEG cannot and is a lossy format. "Lossless" means that, after compression, no data has been removed (or "lost"), while "lossy" means that some data is removed after compression. For audio, MP3s are lossy while WAV files are lossless. You might have also heard of "raw" photos and "raw" videos, those mean that the data is directly from the camera in its original quality.

For most file types, you can't just change the extension to convert them, as the data stored is arranged differently! This is why renaming a .txt file into a .odt will not be a valid rich text document, for example.

If they look the same, you're either using the wrong editor or the wrong font.