Combustion efficiency is a simple (and occasionally misleading) measure of the heating efficiency of a boiler. It is equal to 100 percent minus the percentage of heat lost up the vent (called "flue loss"). The formal methods for measuring flue loss vary by furnace or boiler type, but, in essense, the combustion efficiency measures the total heat energy that is spread through the heating system or escapes from the boiler jacket itself (jacket loss).
Combustion efficiency measures the so-called "steady-state" efficiency of a boiler, and is therefore a less accurate measurement of the overall (or seasonal) efficiency of a boiler than the AFUE. The AFUE takes into account the boiler (or furnace's) efficiency as it cycles through startup and shutdown.
Combustion and thermal efficiency measures are more often used to compare commercial boilers than residential boilers.