Is it "normal" to leave your child w/ another family for a play date?

We have a four year old daughter. She has a friend at school. Her friend’s parents have scheduled two play dates with us, attended two birthday parties, and run into as at a local bar once. We like them, but they aren’t old friends or anything like that. Both play dates have involved this awkward offer by the mom to take our daughter during the play date so that we can do our own thing, run errands, etc. It’s a nice offer, but that is not what a play date is in my mind. I feel like it is odd for her to constantly offer us time to ourselves while she takes our daughter and I think she sees me as odd for refusing.

I do not think we will change our behavior anytime in the near future. I am more interested in social norms. What happens on a “normal” play date?