  We compare stellar photometric variability, as measured from Kepler light
curves by Basri et al. (2011), with measurements of radial velocity (RV)
root-mean-square (RMS) variations of all California Planet Search overlap
stars. We newly derive rotation periods from the Kepler light curves for all of
the stars in our study sample. The RV variations reported herein range from
less than 4 m/s to 135 m/s, yet the stars all have amplitudes of photometric
variability less than 3 mmag, reflecting the preference of the RV program for
chromospherically "quiet" stars. Despite the small size of our sample, we find
with high statistical significance that the RV RMS manifests strongly in the
Fourier power spectrum of the light curve: stars that are noisier in RV have a
greater number of frequency components in the light curve. We also find that
spot models of the observed light curves systematically underpredict the
observed RV variations by factors of ~2--1000, likely because the low level
photometric variations in our sample are driven by processes not included in
simple spot models. The stars best fit by these models tend to have simpler
light curves, dominated by a single relatively high amplitude component of
variability. Finally, we demonstrate that the RV RMS behavior of our sample can
be explained in the context of the photometric variability evolutionary diagram
introduced by Bastien et al. (2013). We use this diagram to derive the surface
gravities of the stars in our sample, revealing many of them to have moved off
the main-sequence. More generally, we find that the stars with the largest RV
RMS are those that have evolved onto the "flicker floor" sequence in that
diagram, characterized by relatively low amplitude but highly complex
photometric variations which grow as the stars evolve to become subgiants.
