I would advise holding off on booking the movers for now, however, and wait to see if your transaction is indeed an average deal. The movers probably will not need much lead time, and you do not want to commit to a date you cannot honor. You should have received a notice explaining this when you first began dealing with the broker in question.
Real property is land and anything attached to the land.
Personal property is everything else. Therefore, anything attached to a dwelling is a fixture and is part of the real estate. Fixtures are generally defined as things that are permanently installed. There are some things that are easily definable as fixtures, such as marble floors or paneling. Other things, like furniture are easily definable as personal property.