In the US, there's a wide variety of boarding arrangements available.
"Full care" is the most typical IME. The barn typically provides hay & grain, and will feed supplements provided by the horse owner. They turn the horse out and bring them in. They may change blankets, put on/off fly masks, hold the horse for the farrier/vet, administer medications, etc. either included in the price or for an added fee. The stalls are typically cleaned once daily by the barn staff.
"Self care" basically provides a space for the horse and little else. The horse owner is responsible for providing the hay and grain and typically must feed it themselves (some places will feed grain if it is prepared by the owner) The horse owner must clean their own stall, provide their own bedding, turn the horse out, and bring the horse in.
"Partial care" can be any combination of responsibilities between full care and self care, depending on the facility. Some consider it "partial care" when the horse owner provides their own hay and grain, but the barn staff provides the rest of the services like you would get in full care. Others are closer to self care, with only a couple of very basic services included.
It's very rare for things like farrier care, vaccinations, deworming, etc. to be included in the cost of even "full care" board.