Vi for Mac OS, differences with Vim
From the vim man page : https://developer.apple.com/library/mac/documentation/Darwin/Reference/ManPages/man1/vim.1.html

There are two vim options to do what you want : 

vim -v          Start Vim in Vi mode, just like the executable was called "vi".   This  only  has  effect
                   when the executable is called "ex".

vim -C          Compatible.  Set the 'compatible' option.  This will make Vim behave mostly like Vi, even
               though a .vimrc file exists.


You can also install ex-vi which is the traditional vi text editor through brew, first install brew http://brew.sh/.
Run brew install ex-vi, but it may cause a conflict with vim.