Skilled nursing is a medicare benefit, not Medicaid. Most NH patients are under medicaid.....long term patients. Some of those patients may require some therapy which would be approved under Medicare (only paying for those therapy minutes) Room and board still falls under Caid. You can be admitted to a NH from a Hospital for skilled care then Medicare will pay for room/board/therapy as long as you meet the intended goals.
Where I live its called rehab. Also rehab and the NH are one and the same. So easier to move from rehab to right into LTC.
Whichever you want to call it, Medicare only pays for a total of 100 days. If its found out that you have hit a plateau within that 100 days, you will be discharged. The 100 days is not guarenteed. Because Medicare only pays for 20 days 100% and 50% 21 to 100, you can apply for Medicaid to pick up the other 50%. As long as you fit the criteria.