The word "public" in "public library" is load bearing, you can't replace it with "regular", hence your confusion.

Private libraries (mine for example) are not free, as in beer or otherwise.

True, though to be fair most people never get to use private libraries. Or they used a library at their University that was technically private, but that gave access to the public as well. Public libraries are ubiquitous and very normal, while private libraries are the exception.

In America, public schools all have private libraries, reserved for attending students. (Maybe some operate as public libraries, but I've never seen nor heard of it.)

Furthermore, public libraries are not necessarily free. In America they virtually are all; fees only for late returns. But this is not globally true; in some parts of the world, libraries open to the public charge a fee for checking out books, or even require a fee for entry.

It's a normal elision, yes, we all picture a public library when we say "library". But "free library" isn't redundant or weird, because "public" is a modifier of library, not a trait.

People tend to call their personal library a "book collection" or the like, but it's a library, in just the same way that a Little Free Library is.

So most people who read have at least a small private library, whether they think of it in those terms or not.

There are two libraries near me that aren’t free - they charge an annual “membership” fee. One even operates more like an old blockbuster when it comes to newly released books. They charge a daily rental fee! It’s 25¢ a day, I believe.

FWIW "Little Free Library" is a trademark and its owners have been aggressive in its defense. I don't know what folks should use as a generic name.

Buurtbieb - in English, roughly pronounced as b-eew-rt-beep.

It's a literal translation of "neighbourhood library", it alliterates, and it sounds cute. (Keep the "beep" part short for that).

Just keep using it as a generic name. They've already lost the generification war. Are they seriously going to track down and sue neighborhood libraries?

Good luck getting a jury to enforce the trademark.

It seems bizarre to me that someone could trademark such a straightforwardly descriptive name.

Yeah, but if you take a book from a LFL, you own it. With a public library, you merely borrowed it.

Obligatory "Free as in beer vs. free as in freedom" comment. I have pulled stuff out of small community bookshelves that would never have seen their chance in a "professional-run" public library, both bad and good.

I always took it to mean “no really this is free, take a book!”