We have investigated the dynamics of water confined in mesostructured porous silicas (SBA-15, MCM-41) and four periodic mesoporous organosilicas (PMOs) by dielectric relaxation spectroscopy. The influence of water-surface interaction has been controlled by the carefully designed surface chemistry of PMOs that involved organic bridges connecting silica moieties with different repetition lengths, hydrophilicity and H-bonding capability. Relaxation processes attributed to the rotational motions of non-freezable water located in the vicinity of the pore surface were studied in the temperature range from 140 K to 225 K. Two distinct situations were achieved depending on the hydration level: at low relative humidity (33% RH), water formed a non-freezable layer adsorbed on the pore surface. At 75% RH, water formed an interfacial liquid layer sandwiched between the pore surface and the ice crystallized in the pore center. In the two cases, the study revealed different water dynamics and different dependence on the surface chemistry. We infer that these findings illustrate the respective importance of water-water and water-surface interactions in determining the dynamics of the interfacial liquid-like water and the adsorbed water molecules, as well as the nature of the different H-bonding sites present on the pore surface.