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.
From the Terminal, you can run:
open -na "Google Chrome"
-n parameters opens a new instance of the application.
Right click on the chrome icon in the tray of your desktop. There will be an option to open new window select this. Open the tabs in the new chrome window you want to have access to and right-click each of them to pin the tabs.