A New York nursing home operates under one license (10 NYCRR Part 415) but often houses two different populations: short-term rehabilitation patients recovering after a hospital stay, and long-term residents who live there permanently. Medicare covers a limited stay of the first kind and essentially never covers the second.
What Medicare's skilled-nursing benefit actually requires
Coverage requires a qualifying inpatient hospital admission -- time spent under "observation status" does not count, even if your parent slept in a hospital bed for two nights. Ask the hospital directly, in writing, whether your parent was admitted as inpatient or held under observation.
Why the same building houses both
Nursing homes are licensed for skilled nursing generally, not separately for short-term rehab versus long-term care -- so the same facility, same staff and same license can serve both populations under one roof.