We investigate the segmental dynamics and glass transition temperature (Tg) of polystyrene (PS) thin films. The former is investigated by alternating current (AC) calorimetry and dielectric spectroscopy (BDS). The Tg, underlying the equilibrium to out-of-equilibrium crossover from the supercooled liquid to the glass, is obtained by differential scanning calorimetry (DSC) and capacitive dilatometry (CD). We show that the intrinsic molecular dynamics of PS are independent of the film thickness both for the freestanding and supported films, whereas Tg decreases with film thickness from several microns down to 15 nm. This result is found for complementary methods and in a simultaneous measurement in BDS and CD. This questions the widespread notion that segmental mobility and the equilibrium to out-of-equilibrium transition are, under any experimental conditions, fully interrelated. For thin films, it appears that the molecular mobility and Tg are affected differently by geometrical factors.