what is the difference between a nurse manager and a nsg supervisor in nursing home?

As you explained it, that is my experience. but, I have also come to find out that each home describes their employees differently.

Where I work... nurse managers are for the day to day running of units and nursing staff. The nurse supervisors are on PM and NOC shifts and all shifts on weekends. There is one designated on those shift for the entire facility. Not just a unit. Either the DON or the nurse manager is on call as a resource and when certain things happen.

I have a Nurse Manager who handles the unit events(audits, staffing, admissions, families), and then a Nursing Supervisor/Charge Nurse for each shift. The Nurse Manager could be AKA a ADON(although we do not have an official job description or call the NM that). The NM takes call with the Administrator, RNAC, and myself on alternating weekends. We are not a big facility though, so I am not sure how the bigger ones would utilize this role.

At my facility, the two units each have a nurse manager who works day shift and functions more along the lines of a charge nurse. There is one evening supervisor for the facility Mon-Fri who sort of does the same as the two managers as well as any chart audits, etc left over from days (I'm the eve supervisor at my facility and I also joke--sort of, not really--about the list of "tasks" the DON gives me each day). There's a weekend supervisor who works 7a-7p for the facility who has pretty much the same responsibities. There's no night supervisor. The nurse managers, ADON, staff educators, MDS, and myself take turns with weekend on-call.

I was an NM. Care plans, families, incidents, staffing, cart when necessary, etc. As supe families, incidents, staffing, cart when necessary, etc.