Troy,
Star diameter appears to vary with star brightness, the FWHM metric on the other hand, because it normalizes flux profiles, tends to give the same number independent of brightness.
Here is the result of my FWHMEccentricity script on a sub taken last year.
The median FWHM is about 1 pixel, which means that one half of a typical star's flux is concentrated within a diameter of 1 pixel. The sub was binned 2x2 with a fairly coarse image scale of 4.2 arcseconds per pixel. Seeing, focus, tracking and collimation were all good, which accounts for the small FWHM value.
Median Eccentricity is a measure of typical star shape, the degree of its roundness or ovalness. Values less than 0.44 are usually considered round.
Of course, FWHM and Eccentricity may vary across the sub due to optical aberrations, tilt, field rotation and what not. The script produces plots to help you see this. You can see that FWHM was slightly higher in two corners.
The script also produces a plot that shows which stars were measured, and also how well the chosen model function fit the star's profile, from negative (better than median fit), to 0 (median fit) to positive (worse than median fit).
The other scripts do similar things, one of them is a batch version, and they also provide information about noise and contrast. For star measurements on single sub I prefer FWHMEccentricity due to its simplicity.
Thanks,
Mike