The apparent horizon is, roughly speaking, the surface at which light rays shined radially outward do not move radially outward (inside the apparent horizon, they move inwards.) This implies that the apparent horizon is a local concept, in the sense that it relies only on an experiment in some small region of spacetime. Furthermore, apparent horizons are coordinate dependent horizons which can change or even vanish depending on your slicing of spacetime.
Event horizons, by contrast, are the surfaces beyond which light can never propagate to null infinity. This definition requires you to know the entire history of the spacetime to determine whether or not the light can escape, and in this sense it is a fundamental causal property of the spacetime which does not depend on coordinates.
Other differences between the two are that apparent horizons, if they exist, are always inside event horizons. The two horizons also coincide for a static spacetime. The apparent horizon can evolve discontinuously, while the EH evolves smoothly.
