So it's an implicit part of your definition of 'library' that they not only house the collection, but that they will not sell books? Or at least that they collect books without intending to ever sell them?

Taxonomy is indeed hard.

In my opinion it comes down to the purpose and reason for existence.

To answer your question I don't think selling a single book makes a library less a library. But if a public lending 'library' had a price tag on every book, I would say it is a bookstore with loans.

In your mind do you consider an iron ore bulk carrier in Australia different from a natural history meusum in France or an iron ore dealer in Argentina? They all store rocks and minerals, including iron ore, and so they could all be called "iron ore storage facilities".

But only one of them has the purpose of studying and preserving artifacts and so it makes sense to create a subclass and call it a meusum.

So, we agree that library is a subset of 'place that collects and stores books'.