We perform a thorough investigation of the drying dynamics of a charged colloidal dispersion drop in a confined geometry. We develop an original methodology based on Raman microspectroscopy to measure spatially resolved colloids concentration profiles during the drying of the drop. These measurements lead to estimates of the collective diffusion coefficient of the dispersion over a wide range of concentration. The collective diffusion coefficient is one order of magnitude higher than the Stokes-Einstein estimate, showing the importance of the electrostatic interactions for the relaxation of concentration gradients. At the same time, we also perform fluorescence imaging of tracers embedded within the dispersion during the drying of the drop, which reveals two distinct regimes. At early stages, concentration gradients along the drop lead to buoyancy-induced flows. Strikingly, these flows do not influence the colloidal concentration gradients that generate them, as the mass transport remains dominated by diffusion. At longer time scales, the tracer trajectories reveal the formation of a gel that dries quasihomogeneously. For such a gel, we show using linear poroelastic modeling that the drying dynamics is still described by the same transport equations as for the liquid dispersion. However, the collective diffusion coefficient follows a modified generalized Stokes-Einstein relation, as also demonstrated in the context of unidirectional consolidation by Style and Peppin [Style and Peppin, Crust formation in drying colloidal suspensions, Proc. R. Soc. A 467, 174 (2011)].