Above the duramater (between the dura and the skull) is a potential space called the epidural space or the extradural space. Bleeding into this area creates a space. It fills rapidly with blood because the bleeding is mostly arterial from the middle meningeal artery, a branch of the middle cerebral. With this type of bleeding an individual may be lucid just after the event and then lapse into a fatal coma.
Beneath the duramater there is another potential space called the subdural space. Bleeding within this space is mainly venous, so it is typically slow. It's often quite dangerous because bleeding can go on all night and cause massive brain damage.
The subarachnoid space between the arachnoid and piamater membranes is filled with cerebrospinal fluid. Bleeding in this space is usually from berry aneurisms.