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

Not to confuse the issue, but for most sources (except a phono stage) a preamp is actually *decreasing* the signal to the amp. Sources like streamers, tuners, cassette decks, CD players, and DACs put out up to 2V on single ended RCA jacks, and up to 4V on XLR. These sources are always at "max" putting out from zero to the maximum voltage to the preamp. 

The preamp acts as a volume control by reducing (limiting) that signal going to the amp. i.e. The reason you need a preamplifier (stand alone or integrated) is so you don't blow the hell out of your speakers without having a volume control. 

On the other hand, a phono stage is doing considerable amplification of the weak signal coming from the cartridge. Back in the old days, separate phono stages were correctly called "phono amplifiers", not "phono preamplifiers". But that point seems to have been lost as many manufacturers call their phono stages "preamplifiers" regardless these days. 

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.