I want to be able to open Chrome on my Mac, and have 2 instances open, each with different tabs.
Is this possible on OS X?
I know on Windows I could do this with Desktop shortcuts.
You do not need two separate instances of Chrome in order to have two windows. OS X works differently than Windows. To open new window in Chrome (or most of the other apps) press ⌘+N. Chrome restores window states after relaunch if You have this option enabled in preferences.