[jhbadger]

There is actually a phrase "free library" commonly seen in older libraries often called a "Carnegie Free Library" because they were created as a philanthropic project by the industrialist Andrew Carnegie. They are called "free libraries" because many libraries in the 19th century were businesses run rather like video stores (if you can remember those) where you had to pay to check out a book, while Carnegie's were free of charge.

[naniwaduni]

Indeed, the Romance cognates of "library" even usually mean bookstore (or maybe bookshelf...etymologically it's just a thing that does something vaguely related to books). Most languages where a cognate of "library" rather than "bibliotheque" means primarily a lending library (which still might be paid) picked it up as a loan from English.

[bombcar]

Many original “libraries” ran on the idea that a book is valuable and rarely new - you’d buy your used copy of Plato, read it, and sell it back for almost what you paid for it. This is infinitesimally different from just renting.