Well, the first difference is non-linguistic: the ghost stays mute and gestures Hamlet on before speaking.
The second is related: Hamlet mentions the ghost crying out even though we don't hear it. In other words, the ghost's language is not always heard.
Turning to the speech itself, when the ghost speaks it is very direct, and key lines are repeated more often than those by the other character. It hammers away at key words like "Swear."