Operation Arrowhead does not contain all of the normal ArmA 2 content within it. If you are looking to launch Combined Ops which is all the content from A2 and all the content from A2OA Steam should give you the option to upon using either shortcut. I would suggest launching Combined Ops ALWAYS if you have both of the games.
Another option would be to get a launcher that is separate from Steam so you don't have to deal with all of Steam's crap. This also allows you to easily modify launch preferences, start with any profile you want, and enable/disable addons easily which would otherwise require a lot of effort and typing with Steam. If you are interested in this route, which I would suggest over the other, just search arma 2 launcher in google and it should be the first link.(Would post a link but this is my first post so I can't)