https://www.paulgraham.com/growth.html
A business is web store selling coffee cups where the bottom line governs it's continuation. A startup is ambitious project where a growth rate governs it's continuation.
The end result of a business is a lemonade stand or a barber or donut shop, the end result of a startup is OpenAI or Google.
a startup makes money selling the startup
That's a bit disingenuous. The more comparable end result for a coffee shop is Starbucks. Or Amazon if you want to talk about books
In fact even the name YC is YCombinator, which in programming is a "function that produces functions" and YC is supposed to be a startup that produces startups. Here Starbucks (Umbrella) is a startup that produces coffee shops (Starbucks).
You can define startup or business however you like it's not a legally protected term. Just around these parts that's what it means and I personally find the distinction useful when reasoning about what does and doesn't have high growth potential.