These are terms that federal regulations and states use to decipher between two different service-delivery models. The exact words may be different from state to state but the concept is the same.
A) In a provider-owned or controlled setting, the home is owned or rented by the residential service provider. Therefore, residents who live in that home cannot change providers and stay in that particular home setting. If residents of provider-owned or controlled settings want to move for any reason, they may or may not be able to keep the same service provider and staff.
B) In a consumer-owned or controlled setting, the home and service provision are disconnected. In other words, a resident owns or rents their chosen home from a landlord who is not their mandatory service provider. The resident of a consumer-owned or controlled setting can choose from a variety of service providers and can switch providers at anytime without having to leave their home. They could also move to another home and keep their service provider and maybe even staff because their supports are built around their needs and not tied to a particular residence.