I'm not a programmer so I'm tending towards accepting HTML as a programming language, because it's a language you type in to make the computer do stuff. Is there maybe another example of something that does what HTML does but obviously isn't a programming language?
Markup language vs programming language is similar to the difference between a font and a typeface. Sure, they're different but to the layperson, they might as well be the same thing.
A PowerPoint, word document or even a text file or picture. There is only a description in the file of what it holds and it's up to the program that reads it, how it will visualize or interpret it.
A word document can also contain a script, as can html pages. It's why I thought these two were the closest match. Nobody is going to call those programming languages.
Yes, typing <p> in HTML is like pressing enter in word, but that doesn't make it a programming language, it makes it a markup language.
A markup language is also what you can use to format comments here: You use a specific syntax to indicate how you want things formatted.
The separation from a programming language is that a programming language can be used to implement logic, like saying: In the following paragraph, a word should be bold if it contains the letter "A". That cannot be done with a markup language.
A markup language (which is what HTML is) is like an advanced text container. When you write a post or comment here, you can use specific syntax to indicate the size of the text, a hyperlink, a quote, etc. HTML is that. It doesn't "do" anything, you're just writing in what you want it to display, and that is displayed.
A programming language lets you somehow "do" something. Instead of declaring explicitly "write this text in bold" a programming language can be used to process all the text in an arbitrary document, and change the word "aeroplane" to bold whenever it turns up. That is: The output from the code isn't just a rendering of what is explicitly written there, which is what a markup language gives you.