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We analyze the gas kinematics of damped Lya systems (DLAs) hosting high zgamma-ray bursts (GRBs) and those toward quasars (QSO-DLAs) focusing onthreestatistics: (1) dv, the velocity interval encompassing 90% of thetotaloptical depth, (2,3) Wsi and Wciv, the rest equivalent widths of theSiII1526 and CIV1548 transitions. The dv distributions of the GRB-DLAs andQSO-DLAs are similar, each has median dv~80km/s and a significant tail toseveral hundred km/s. This suggests comparable galaxy masses for the parentpopulations of GRB-DLAs and QSO-DLAs and we infer the average dark matter halomass of GRB galaxies is <~10^{12} Msol. The unique configuration of GRB-DLAsightlines and the presence (and absence) of fine-structure absorption togethergive special insight into the nature of high z, protogalactic velocity fields.The data support a scenario where the dv statistic reflects dynamics in theinterstellar medium (ISM) and Wsi traces motions outside the ISM (e.g. halogas, galactic-scale winds). The Wsi statistic and gas metallicity [M/H] aretightly correlated, especially for the QSO-DLAs: [M/H]=a + b log(Wsi/1A) witha=-0.92+/-0.05 and b=-1.41+/-0.10. We argue that the Wsi statistic primarilytracks dynamical motions in the halos of high z galaxies and interpret thiscorrelation as a mass-metallicity relation with very similar slope to the trendobserved in local, low-metallicity galaxies. Finally, the GRB-DLAs exhibitsystematically larger Wsi values (>0.5A) than the QSO-DLAs (<Wsi>~ 0.5A) whichmay suggest galactic-scale outflows contribute to the largest observed velocityfields.Comment: 14 pages, 9 figures. Submitted to Ap

On the Nature of Velocity Fields in High‐zGalaxies