Canonicity is a fundamental notion in classical modal logic and other logics for which semantics based on relational structures are available, since it provides the main proof path towards completeness results. Thanks to duality theory, canonicity can be investigated both in an algebraic and in a frame-theoretic setting. The existing canonicity results have been obtained by means of one of the following two approaches, here respectively referred to as the canonicity via-correspondence approach, and the J´onsson-style approach. In this talk we are going to compare these two approaches, and show that the two approaches use essentially the same order-theoretic properties, but in two different ways.