Using solar soft X-ray irradiance measurements from the SXP instrument on the SNOE satellite, we relate the solar surface flux densities and their variability to those of stars as measured with the PSPC instrument on ROSAT. We translate SNOE-SXP measurements into equivalent ROSAT-PSPC counts using model spectra calculated from the CHIANTI package. Using the SNOE-SXP measurements has significant advantages over earlier studies: the absolute calibration is known to +/-25%, SNOE measures the Sun as if it were an unresolved star, it has operated over a significant fraction of the solar cycle, and its three wavelength channels overlap substantially with that of the ROSAT-PSPC instrument. The predicted solar X-ray luminosities and surface flux densities are compared with measurements from the ROSAT database. We find that we can estimate the luminosity of the Sun as seen in the 0.1-2.4 keV (``RASS'') passband of ROSAT-PSPC to within +/-50%, not counting sources of systematic uncertainty mentioned in an appendix: the result lies between 1027.1 and 1027.75 ergs s-1 (measured in the existing data set, only partially covering a full solar cycle) and between 1026.8 and 1027.9 ergs s-1 (extrapolated to the full activity range of a typical solar cycle). The solar luminosities lie close to the median behavior found for a volume-limited (d<13 pc) sample of G stars studied in 1997 by Schmitt, revealing the Sun to be a normal or slightly inactive G dwarf. A factor of 1.5 peak-to-peak variation in the RASS passband is predicted due simply to rotational modulations (i.e., those filtered to include periods P<81 days). The ratio of maximum/minimum RASS luminosities from the magnetic activity cycle (filtered to include periods P>81 days) are estimated to be 0.7-0.8 in log10LRASS, a ratio of 5 or 6. These variations are much smaller than both recent estimates of solar X-ray variability and the range of X-ray luminosities seen within Schmitt's sample. It is suggested that the reported absence of ``solar-like'' cyclic emission in stellar X-rays might partly arise because the Sun is less variable than assumed in some earlier work. Repeated ROSAT observations of α Cen A during 1995-1998 show X-ray behavior reminiscent of the Sun during activity minimum conditions.