The states and electrosorption isotherms for underpotential deposited (UPD) H on Pt single-crystal surfaces are highly specific to the surface lattice geometry. In the present paper we show that the corresponding kinetics of the UPD processes are surface dependent and can be distinguished, in some cases, from the kinetics of partial charge transfer in coadsorption of HSO4- ions. Based on the known wide range of exchange current-densities for the H-2 evolution reaction (HER) at a variety of metals, it would be expected that the HER kinetics, involving overpotential deposition (OPD) of H, would also be sensitive to electrode surface geometry, a result surprisingly not found in some recent and earlier works. It is shown that this conclusion is due to the actual surface-dependent kinetics being obscured by effects associated with H-2 diffusion from a supersaturated interphasial layer. When the diffusion effect is factored out by means of impedance spectroscopy (IS) measurements at rotated single-crystal Pt surfaces, quite substantial dependences of the HER kinetics and Tafel relations on cathode surface structure are revealed, as well as surface-specificity of the IS behaviour. Possible relations between the kinetics of the H UPD and the HER OPD processes are examined in relation to site occupancies by UPD and OPD H.