ViM is just Vi iMproved. They share most their keybinds but VIM has the whole plugin architecture thing.
This is a big sticking point for a lot of VIM users [1]. If you ever end up on a Unix box that doesn't have VIM, you can always fall back on Vi.
[1]: /users/religious fanatics/
zck@zck-desktop:~$ vi --version
VIM - Vi IMproved 7.4 (2013 Aug 10, compiled Jan 2 2014 19:39:32) $ vi --version
vi: illegal option -- -
Usage: vi [- | -s] [-l] [-L] [-R] [-r [file]] [-t tag]
[-v] [-V] [-w size] [+cmd | -c cmd] file...
$ pacman -Qi vi
Name : vi
Version : 1:070224-2
Description : The original ex/vi text editor
Architecture : x86_64
URL : http://ex-vi.sourceforge.net/
Licenses : custom:ex
Groups : base
Provides : None
Depends On : ncurses
Optional Deps : s-nail: used by the preserve command for notification [installed]
Required By : None
Optional For : None
Conflicts With : None
Replaces : None
Installed Size : 290.00 KiB
Packager : Evangelos Foutras <evangelos@foutrelis.com>
Build Date : Sun 06 Sep 2015 03:34:15 PM EDT
Install Date : Fri 18 Sep 2015 10:33:33 PM EDT
Install Reason : Explicitly installed
Install Script : No
Validated By : Signature
root@dicks:~# which vi
/usr/bin/vi
root@dicks:~# file /usr/bin/vi
/usr/bin/vi: symbolic link to `/etc/alternatives/vi'
root@dicks:~# file /etc/alternatives/vi
/etc/alternatives/vi: symbolic link to `/usr/bin/vim.basic'
root@dicks:~# file /usr/bin/vim.basic
/usr/bin/vim.basic: ELF 64-bit LSB executable, x86-64, (snip)
root@dicks:~# vi --version
VIM - Vi IMproved 7.4 (2013 Aug 10, compiled Jan 2 2014 19:39:32)