In law, continuance means the adjournment of a proceeding to a later time. In other uses, continuance and continuation are generally interchangeable: one may refer to the continuation or the continuance of a state of war or period of drought. However, continuation means "the extending or prolonging of time or space": the continuation of a structure might involve adding a room or wing, whereas the continuance of that structure would refer to the period of its existence, its time of standing. Thus you might speak of a politician's continuance in office and the continuation of the process by which he is elected.
Dictionary of problem words and expressions. Harry Shaw. 1975.