I would say that 'drought' is a period with particularly low precipitation and/or high evapotranspiration, which can be sometimes compared with the long term average of the site over the same period. Then, 'hydric deficit' is the effect of drought on the water reserve (e.g., soil water deficit) as the difference between the max (e.g., field capacity) and the actuel water availability. Finally, 'water stress' refers to the physiological responses of plants (or other organisms) to hydric deficit, which depend on ecological water strategy. However, the definitions may vary a bit according to the scientific community and the scale considered.