Hi,
Right, some are FITS images, some are FITS tables, and some are just FITS headers. On the
nova.astrometry.net site, if you look at a solved image, for example, this recent one,
http://nova.astrometry.net/user_images/1770829the "new-image.fits" link is a FITS image with a WCS header. If you open that up in the SAO ds9 program (
http://ds9.si.edu/site/Home.html), you'll get RA,Dec coordinates along with x,y coordinates as you move around the image.
The "wcs.fits" file is a FITS header -- 80-character lines of text describing the WCS (World Coordinate System), or mapping between x,y and RA,Dec.
The "rdls.fits" and "axy.fits" files are FITS tables, listing RA,Dec coordinates of reference-catalog stars, and X,Y coordinates of stars detected in your image, resp. They can be viewed using the "tablist" program (included in the Astrometry.net source code), or read in using your favorite programming language. The "corr.fits" is a table listing stars that we think match between your image and the reference catalog.
Hope that helps!
--dustin