We present an analysis of high resolution Chandra spectra of late-type stars. Our sample includes giant stars from the Hetzsprung gap to the ''clump'' phase, active stars that have similar fundamental parameters but which have followed quite different evolutionary paths, and RS CVn binary systems. Using a new technique based on the ratios of prominent lines of highly ionized Fe and resonance lines of He-like and H-like ions, we have determined the temperature structure and chemical composition of the emitting plasma in their coronae. We find similarities in the temperature structure within each group of stars but differences between groups. The single giants tend to show a featureless and smooth temperature structure while for the active binaries there is evidence of more complex temperature structure. The single giants show a solar-like FIP effect, despite their clear non-solar evolution and internal structure. In contrast, the active binaries and dwarfs exhibit enhancements of high FIP elements such as Ne and Ar, and show some evidence that elements with very low FIP, such as Na,Al and Ca are enhanced relative to Mg, Si and Fe that have slightly higher FIP. We discuss the results in the context of models of coronal heating and chemical fractionation. DGA and WB were supported by Chandra grants GO1-2006X and GO1-2012X. LL was supported by NASA AISRP contract NAG5-9322. JJD and VK were supported by NASA contract NAS8-39073 to the Chandra X-ray Center.