vim is the improved version of vi, which is the visual interface to ex, which is the extended editor ed... the one true editor ( https://www.gnu.org/fun/jokes/ed-msg.txt )

You will not infrequently find vim and vi links to the same executable.

    /usr/bin % ls -l ex vi vim
    lrwxr-xr-x  1 root  wheel        3 Aug 24 03:59 ex -> vim
    lrwxr-xr-x  1 root  wheel        3 Aug 24 03:59 vi -> vim
    -rwxr-xr-x  1 root  wheel  5155568 Aug 24 03:59 vim

The difference between which way you have argv[0] slightly changes the functionality... but it's the same thing.

ed remains its own thing.

    /bin % ls -l ed
    -rwxr-xr-x  1 root  wheel  235296 Aug 24 03:59 ed

THE MIGHTY ED HAS SPOKEN!!!

?

To expand on shagie's answer, vi is a separate utility except when it's not (f.g. Linux vi is usually a minimal vim build running in vi-compatible mode). For a more pure taste of vi, install nvi or use vi on *BSD.

In vim there are a lot of emacs-like plug-ins that reimplement functionality found elsewhere.

You can still use the vi style workflow though.