Right, IAP means "Istrebitel´nyy Aviastionyy Polk" = Fighter Aviation Regiment, Gv "Gvardiya" = Guards.
The guard titel was given, as RIPTIDE mentioned, for good performance and was mostly accompanied with special treatment, which means decent equipment and supplies. Especially in 2ndWW regiments were treated that way. For example 88 IAP, which in 1944 became GvIAP, was equiped with the promotion with La5FN, before they flew I-16!
Found something more in a book of mine
The latter must have changed later, see my example with 88 IAP.