The dynamics of coalescence of two water sessile drops is investigated and compared with the spreading dynamics of a single drop in partially wetting regime. The composite drop formed due to coalescence relaxes exponentially toward equilibrium with a typical relaxation time that decreases with contact angle. The relaxation time can reach a few tenths of seconds and depends also on the drop size, initial conditions, and surface properties (contact angle, roughness). The relaxation dynamics is larger by 5 to 6 orders of magnitude than the bulk hydrodynamics predicts, due to the high dissipation in the contact line vicinity. The coalescence is initiated at a contact of the drops growing in a condensation chamber or by depositing a small drop at the top of neighboring drops with a syringe, a method also used for the studies of the spreading. The dynamics is systematically faster by an order of magnitude when comparing the syringe deposition with condensation. We explain this faster dynamics by the influence of the unavoidable drop oscillations observed with fast camera filming. Right after the syringe deposition, the drop is vigorously excited by deformation modes, favoring the contact line motion. This excitation is also observed in spreading experiments while it is absent during the condensation-induced coalescence.