Is there a clear definition of what "Integrated" means?

It's an evolved meaning. Longer time ago there was just an amp whether it's preamp or poweramp.

I think the definition has been blurred by market changes- in the early '70s, an integrated amp was power amp plus mostly full featured preamp with tape loop, sometimes tone controls, and other features characteristic of preamps at the time-- possibly even a phono stage. With the rise in popularity of digital sources and a range of tube amps (I'm more familiar with those than SS) containing volume controls and often more than one input with selector, such an amp can make a separate preamp stage unnecessary. I'm not sure there is a single definition of "integrated amp" for this reason--I used to think of them as "receivers" without the tuner section. My take, fwiw. 

@whart Well this touches on why I am asking. If I look up most tube amp designs, PP, SE, and a variety of power tubes, the designs usually include the input stage: There is some twin triode doing some initial amplification usually, and discussions of coupling capacitors or transformer coupled etc. This includes guitar amps, too.

So, are these all tube integrated amps? Because nobody really calls them that, just "tube amps". But it kind of makes sense, if so.

Haven’t seen the word resistance yet. Cleaning up the signal so a constant load is presented to the power amp section - allowing it to run in optimal parameters - I thought was the point of a preamp. The input can have varying voltage and resistance, but the power amp doesn’t see any of that. 
 

This is a tricky concept since we always talk about the voltage of the source but rarely the resistance.  

I've always viewed Integrated amps as essentially the predecessors to receivers, because we used to use external tuners.  I think the inclusion of a pre-amplification stage as a qualifier is debatable as a pre-amplifier typically came just before the power amplifier and did not necessarily include more than one input channel, but in the late 70's we started to see many more pre-amplifiers that served as our connectivity as an integrated amplifier would, sans the main amplification stage.

My definition of an Integrated amp is a power amplifier that allows for switchable connectivity to more than one input.