All four of
/dev/pts/2 are file names, as are
/fioejfoeijf, etc. All but that last example are likely to be the name of an existing file on your machine. A file name is a string that can designate a file on your filesystem; under Linux, any string that does not contain a null byte and that is at most 4096 bytes long is a valid file name. Many of these names are equivalent, e.g.
/bin/sh is equivalent to
/bin is an existing directory), etc. All the examples I've given so far are absolute file names; there are also relative file names, which do not begin with a
/ and whose meaning depends on the current directory.
The terminology surrounding file names isn't universal; sometimes “file name” means a full path to a file, and sometimes it means the name of a directory entry. The POSIX terminology is “filename” or “pathname component” for the name of a directory entry, and “pathname” for a full path.
A file descriptor designates an open file in a particular process. The kernel maintains a table of file descriptors for each process. Each entry in the file descriptor table indicates what to do if the process requests reading, writing and other operations on the file descriptor.
File descriptors may correspond to a file and have an associated name, but not all of them do. For those that do, the file may be a regular file, a directory, a device file or a named pipe (also called FIFO) (the kind created by
mkfifo); some systems have further possibilities such as Unix sockets and doors. Examples of file descriptors that don't have an associated named file include pipes (the kind created by the
pipe system call) and networking sockets.
/proc/self/fd/0 are file names (all equivalent) with a peculiar meaning: they all designate whichever file is currently accessed via file descriptor 0. When a process opens these, the kernel copies the entry with index 0 in the file descriptor table to a new descriptor. Opening any of these files is equivalent to calling
dup(0). The named files are a way to indirectly get a process to use one of its already-open files rather than open a new file; they are mostly useful to pass on a program's command line, where the program expects the name of a file to open.