It could be unique to me, or my social circle, or my geography, but I've often heard and said "house sitting" when just popping in for a friend.
1: You busy this afternoon?
2: I am from 3 to about 4; I'm house sitting for my neighbors while they're in Orlando.
I would never say pet sitting here, if I was popping in and out. To me, pet sitting means full time care; either the pet is with me, or I am staying over pretty much full time to keep the pet company and to fill the vacant house. Also, while I'm sure someone somewhere in the US will charge for house sitting, I've never come across it. Pet sitting (and boarding and walking), on the other hand, is a thriving business.