I offer specifically, but only about things I'm not directly looking at. If someone says, "Is there anything I can do?" it can be harder to accept because it kind of sounds like a formality, not a real offer. So if I come over, and we've only been in the living room, I'll say something like, "Can I help you at all? You want a room vacuumed? Some dishes washed?" I don't think I'd look directly at a basket of laundry and ask to fold it unless I was at a good friend's house.