What is the difference between long term acute care hospitals rehabilitation hospitals and skilled nursing facilities?

If a person needs active hospital treatment for wounds or surgeries that are long term but ongoing they would be in an acute care hospital. Once the surgeries were over and wounds were healing they may need physical therapy to rehabilitate their ability to walk, use their hands/arms/fingers, dress themselves or variations of the same but also they need nursing care. In this case they would transfer to a skilled nursing rehabilitation facility until they could strengthen enough to go home. If the person could not be rehabilitated to go home due to their physical or mental state then they would transfer to a long term nursing home where the emphasis is on caring for basic needs more than medical needs. The care is matched to their needs for feeding and bathing and they are visited by a doctor once a month.