Yes, there is a difference. To orbit means to hold at one's present position, i.e. to fly in circles until further advised. To make a three sixty means to complete a full circle and proceed further once the circle has been completed.
Both instructions can be combined with a direction of turn (MAKE A THREE SIXTY TURN LEFT [or RIGHT], respectively ORBIT LEFT [or RIGHT]).
Reference: PANS-ATM 6.5.5.10 and 12.4.1.5.