Could be a Cap coat or a thin coat is sometimes called a skim coat or feather coat

I use basic drywall primer over all of those.

They are the same thing. A skim means just a thin finishing coat of plaster about 3mm or so thick, just enough to cover any minor imperferctions on the wall.

Cut it out then put a skim coat of mud over it.

Delivery is sometimes used to refer to the stage in building construction where the building is available to the user. This can be completion, or can be before completion of construction.