We compare high-resolution ultraviolet spectra of the Sun and thirteen solar-mass main sequence stars with different rotational periods that serve as proxies for their different ages and magnetic field structures . In this the second paper in the series , we study the dependence of ultraviolet emission-line centroid velocities on stellar rotation period , as rotation rates decrease from that of the Pleiades star HII314 ( P _ { rot } = 1.47 days ) to \alpha Cen A ( P _ { rot } = 28 days ) . Our stellar sample of F9 V to G5 V stars consists of six stars observed with the Cosmic Origins Spectrograph on HST and eight stars observed with the Space Telescope Imaging Spectrograph on HST . We find a systematic trend of increasing redshift with more rapid rotation ( decreasing rotation period ) that is similar to the increase in line red shift between quiet and plage regions on the Sun . The fastest-rotating solar-mass star in our study , HII314 , shows significantly enhanced redshifts at all temperatures above \log T = 4.6 , including the corona , which is very different from the redshift pattern observed in the more slowly-rotating stars . This difference in the redshift pattern suggests that a qualitative change in the magnetic-heating process occurs near P _ { rot } = 2 days . We propose that HII314 is an example of a solar-mass star with a magnetic heating rate too large for the physical processes responsible for the redshift pattern to operate in the same way as for the more slowly rotating stars . HII314 may therefore lie above the high activity end of the set of solar-like phenomena that is often called the “ solar-stellar connection ” .