On May 23, 2006 we used the ACIS-S instrument on the Chandra X-ray Observatory (CXO) to study the X-ray emission from the B fragment of comet 73P/2006 (Schwassmann-Wachmann 3) (73P/B). We obtained a total of 20 ks of CXO observation time of Fragment B, and also investigated contemporaneous ACE and SOHO solar wind physical data. The CXO data allow us to spatially resolve the detailed structure of the interaction zone between the solar wind and the fragment's coma at a resolution of ~ 1,000 km, and to observe the X-ray emission due to multiple comet--like bodies. We detect a change in the spectral signature with the ratio of the CV/OVII line increasing with increasing collisional opacity as predicted by Bodewits \e (2007). The line fluxes arise from a combination of solar wind speed, the species that populate the wind and the gas density of the comet. We are able to understand some of the observed X-ray morphology in terms of non-gravitational forces that act upon an actively outgassing comet's debris field. We have used the results of the Chandra observations on the highly fragmented 73P/B debris field to re-analyze and interpret the mysterious emission seen from comet C/1999 S4 (LINEAR) on August 1st, 2000, after the comet had completely disrupted. We find the physical situations to be similar in both cases, with extended X-ray emission due to multiple, small outgassing bodies in the field of view. Nevertheless, the two comets interacted with completely different solar winds, resulting in distinctly different spectra. ; Comment: accepted by ApJ, 44 Pages, including 4 tables and 14 figures