We experimentally investigate the coalescence between two droplets with different sizes in the surrounding water via high-speed visualization. We identify three coalescence patterns by clarifying the dynamic interface evolutions, including liquid bridge evolution, capillary wave propagation, and pinch-off behaviours. The results indicate that the coalescence patterns are directly related to the propagation of capillary waves on the coalescent droplet, which is governed by the competition among the capillary force, viscous force, and inertia involved in the draining from the original droplets into the liquid bridge. The external water can efficiently damp the oscillation in capillary wave propagation after the coalescence. In the inertial regime after the droplet coalescence, the evolution of liquid bridge is observed to follow a linear scaling law, when the capillary force induced by the azimuthal interface of the liquid bridge drives the liquid bridge expansion. Accordingly, a phase diagram is organized to characterize these coalescence patterns depending on Ohnesorge number, relative viscosity between external water and droplet, and size ratio between two coalesced droplets.