One thing I'm not sure if anybody mentioned... at least in the systems I worked at in Maryland, librarians *don't* check out books! I know, crazy, right? But checking out books is, well, not generally skilled labor. So the people who shelve books and check them out to you are circulation assistants or pages. In my system, the difference between the two was that a page was a minimum-wage job, mostly high school kids, and they *only* shelved books. Circulation assistants shelved books, checked books out, helped fill orders for hold books (books requested by different branches in the system) or ILL (inter-library loans, books requested by different library systems), deleted weeded books from the library system (librarians would decide what books the library no longer wished to keep, the circulation assistants would then delete them from the system and send them down to be sold in book sales or the bookstore), things like that.
Librarians were the ones who answered reference questions, weeded books, organized storytimes, book discussions, special events and programming, book displays, requested new books to be ordered, ran the volunteer programs, dealt with discipline and other patron issues, helped with the computers, helped use other machines like copiers and microfiche, attempted to find somebody who spoke the language of a patron, helped patrons with database enquiries and such, etc.
In Maryland, there were "actual librarians," who had Master's degrees, and "library associates," who acted like librarians but only had a bachelor's and had a cap as to how far they could advance without a degree. They couldn't move into a position where they would supervise other people, but they did most of the other stuff listed on my "librarians" list of duties.
Librarians checking out books tends to be something you'd see more in a small library, where a few staff members do everything. But in larger libraries, tasks tend to be diversified between the "circulation staff" and the "reference staff." And sometimes reference is split into "adult" and "children's" or even "young adult." All depends on the size of the library and staff.