According to my Order of Battle Vietnam, the "AW" stands for Automatic Weapons. It calls these units "Artillery" not differentiating them from "Field" Artillery, but the distinctive unit insignia they show is definitely from the ADA regimental system, not FA.
"AW" is what gun ADA units were called prior to ADA. Scroll to the bottom of the page.
What's really funny to me and a bit of a mystery, is the Distictive Unit Insignia (often erroneously referred to as unit crest) that they show for the 5/2 Artillery on this page.
If you compare the DUIs for the other two units (44th Arty and 60th Arty in Vietnam) to the 44th ADA and 60th ADA, you'll see they are the same, so clearly these were ADA units.
But there's something funny with the 2nd Artillery. If you look up the 2nd ADA, that's not the DUI you will find.
HOWEVER, notice the motto on the bottom "The Second First". Not only is that the same motto as the 2nd FIELD Artillery, but that exact DUI is what members of 1st Bn 2nd Field Artillery were wearing until sometime in late 1971 or 1972 when they switched to the current DUI which depicts an artillery pack mule. The reason I'm aware of this is that I was assigned to 1st Bn, 2nd Field Artillery in Oct 1972, and earlier in the year, I got a welcome letter from the unit on letterhead stationery with the older DUI on it.
So either the 2nd ADA changed their DUI, and 2nd Artillery in Baumholder went from 2nd ADA to 2nd FA, or the unit in Vietnam was actually 2nd FA and THAT unit changed their DUI to the current one.