Relative File Names

All the directories in the file system form a tree starting at the root directory. A file name can specify all the directory names starting from the root of the tree; then it is called an absolute file name. Or it can specify the position of the file in the tree relative to a default directory; then it is called a relative file name. On GNU and other POSIX-like systems, after any leading ‘~’ has been expanded, an absolute file name starts with a ‘/’ (see abbreviate-file-name), and a relative one does not. On MS-DOS and MS-Windows, an absolute file name starts with a slash or a backslash, or with a drive specification ‘x:/’, where x is the drive letter.

— Function: file-name-absolute-p filename

This function returns t if file filename is an absolute file name or begins with ‘~’, nil otherwise.
          (file-name-absolute-p "~rms/foo")
               ⇒ t
          (file-name-absolute-p "rms/foo")
               ⇒ nil
          (file-name-absolute-p "/user/rms/foo")
               ⇒ t

Given a possibly relative file name, you can expand any leading ‘~’ and convert the result to an absolute name using expand-file-name (see File Name Expansion). This function converts absolute file names to relative names:

— Function: file-relative-name filename &optional directory

This function tries to return a relative name that is equivalent to filename, assuming the result will be interpreted relative to directory (an absolute directory name or directory file name). If directory is omitted or nil, it defaults to the current buffer's default directory.
On some operating systems, an absolute file name begins with a device name. On such systems, filename has no relative equivalent based on directory if they start with two different device names. In this case, file-relative-name returns filename in absolute form.
          (file-relative-name "/foo/bar" "/foo/")
               ⇒ "bar"
          (file-relative-name "/foo/bar" "/hack/")
               ⇒ "../foo/bar"

25.9.2 Absolute and Relative File Names