I can't see owning a cow without a place to keep them unless it was a kid who showed them in 4H or FFA since there is no other purpose other than to eat them or get milk from them. I also think there are exceptions such as a wildfire that would cause some to be displaced but other ranchers are usually considerate enough if they have available pasture to let someone keep their cattle on it while replacing fence etc.
I've never heard of boarding cattle unless it was a show stock but a lot of people lease pasture usually pay for the lease annually but the owner of the cattle or horses for that matter is responsible for their own livestock, upkeep on the lease etc. If fence gets damaged they have to fix it, it isn't like boarding facilities where someone else typically does all the dirty work for you
I would call it boarding per say, but more leasing land. We have over 100 acres when I lived in Europe and we had a guy who leased a lot of the land we owned for his cows. He would hay it and come bring his cows over.
My dad raised steers and beef when I was growing up- but I wanted to show Jerseys for 4-H. So I started with a couple calves and when the time came for them to calve themselves we would have her calf at our place and then we would hand milk for a couple days (the colostrum for the calf) and we would walk her over to the neighbors milking barn and he would feed her and take care of her for the exchange of the milk. It worked for me because I had a cow to show and keep records on and his butter fat count went up!!! Anyways we did this with 4 heifers/ cows.