During its 2yr Prime Mission, TESS observed over 232000 stars at a 2min cadence across ~70% of the sky. These data provide a record of photometric variability across a range of astrophysically interesting timescales, probing stellar rotation, stellar binarity, and pulsations. We have analyzed the TESS 2 minute light curves to identify periodic variability on timescales of 0.01-13days, and explored the results across various stellar properties. We have identified over 46000 periodic variables with high confidence, and another 38000 with moderate confidence. These light curves show differences in variability type across the Hertzsprung-Russell diagram, with distinct groupings of rotational, eclipsing, and pulsational variables. We also see interesting patterns across period-luminosity space, with clear correlations between period and luminosity for high-mass pulsators, evolved stars, and contact binary systems, a discontinuity corresponding to the Kraft break, and a lower occurrence of periodic variability in main-sequence stars on timescales of 1.5-2 days. The variable stars identified in this work are cross-identified with several other variability catalogs, from which we find good agreement between the measured periods of variability. There are ~65000 variable stars that are newly identified in this work, which includes the rotation rates of low-mass stars, high-frequency pulsation periods for high-mass stars, and a variety of giant star variability.