Can driver for some device (for example LCD display), also be called library (a set of functions for work with)? If not what is the difference, and what term is used for what?
The term "library" is generally used for something that is written once, and used (or at least written as if it is to be used) more than once, often by someone that is not its original author.
The term "device driver" is genrally used for a piece of software that handles the specifics of one device (a piece of hardware).
In most cases a device driver will be a library, but you could write a device driver specifically for one project.
A library can do other things than handling a device, for instance a data compression library.