We present detailed studies of segmental dynamics and viscosity in polystyrene (PS) and poly(2-vinylpyridine) (P2VP) with different molecular weights (MW). Analysis reveals that the molecular weight dependence exhibits very different temperature scaling for segmental and chain dynamics: while segmental relaxation in samples with different MW forms a master curve when presented vs T - Tg, the viscosity of the same samples falls on a master curve when presented vs Tg/T (here Tg is the glass transition temperature). This result indicates significant difference in the friction mechanisms for chain and segmental dynamics. Even more puzzling is that the absolute values of viscosity appear to be essentially MW independent when presented vs Tg/T up to surprisingly high molecular weight. In particular, viscosity at T-g does not show any appreciable molecular weight dependence up to MW approximate to 30 000 g/mol. We speculate that molecular scale relaxation (chain dynamics) in polymers behaves similar to the structural relaxation in small molecular liquids, while additional slowing down mechanism contributes to the segmental relaxation in the same polymers.