We live in Maryland. There is no lease agreement. Family friend lives in our guest house pays utilities not charged rent. Has lived there 3 years. Gave them 30 day verbal notice and they agreed to leave. They did not leave. How does the state see their status? A tenant? Can they be considered week to week or month to month? Thanks for your help

Yes, they are considered a tenant. Since they don't pay a rental, they would be a month to month tenant. Also, since they don't pay a rental you can't evict them for non payment.

So you need to give them a WRITTEN notice that you are terminating their tenancy in 30 days. If they are not out within that time you go to court to start the eviction process.