mahnertree,
I've just had my 011 AV apart for the first time since I bought it, unrunning, with the house.
The one with the fitting is the "vent tube;" it has a little set screw inside it (or should have) to retard the flow of raw gas out when the saw is up-ended but nevertheless to let air back in. That tube vents into the clutch area through a squarish opening in the corner behind the carb. On mine, although rotted, a piece of foam filter was zip-tied around the end, and that filter is hidden behind a gold-colored metal shield you can see with the blade shroud off. The shield is held on with one scrench-sized bolt, which is deep in a hole underneath it, and probably hidden by sawdust and oil.
The other hole should have a tube coming from the (fuel filter on the bottom of the) fuel tank; that's a much longer tube, and that's the one that connects to the fitting on the carb, just above where the vent tube exits.
Capiche?