I'm inclined to think of an ordinary (single stage) gas furnace as one which when operating is able to burn gas and produce heat at one rate. Implementation wise, I think of a single burner "stage" that is simply turned on for awhile and then turned off for awhile.
I'm inclined to extend that definition to multistage gas furnaces, and believe that a N-stage gas furnace is one which when operating can burn gas and produce heat at N different rates and while running can switch between those rates as deemed necessary by some kind of logic. Implementation wise, I think of multiple burner stages that can be independently turned on and off. In practice I imagine (residential) N-stage gas furnaces to have but a tiny number of stages and thus be limited to a tiny number of output rates.
I'm inclined to think of a modulating furnace as one which can output at MANY different rates because it [also] has a gas solenoid valve with a wide range of settings.
I think, based on my own perhaps flawed "definition", that modulating > N-stage > ordinary single stage because I think a furnace which can better match output to demand has some advantage when in comes to providing comfortable regulation of temperature. More specifically, I imagine a 2-stage furnace that can output at only 36000 or 56000 vs a modulating furnace that can output at many different levels between and including 36000 and 56000. In a home that is experiencing a 44000 BTU/Hr heat loss. My "modulating furnace" is theoretically able to output at or close to the 44000 BTU/Hr required. It is able to meet demand without creating more hot feeling air and/or noise than is necessary. Whereas the 2-stage furnace will, for a time at least, output at an output level that is significantly greater than necessary. It will for a time exceed demand and create unnecessarily hot feeling air and more noise than is necessary.
Is my thinking sound? Am I overlooking something, such as the ability of some multistage furnaces to duty cycle furnace stages so as to achieve intermediary levels of heat?
I realize that when it comes to regulation and providing comfortable conditioning, there is more to it than just the "raw" output capabilities of a furnace. However, I am hoping that my basic view of a modulating furnace isn't fundamentally flawed. Comments? Thanks.