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

but what constitutes the "pre-amp"? 

Who cares???  If you have an amp that has a volume control it’s an integrated amp. It matters not if the preamp section is active or passive, it’s still an integrated amp. 

but what constitutes the "pre-amp"?

my guess is the "pre"?

“A preamplifier, often abbreviated as preamp, is an electronic device that amplifies a weak electrical signal to a level that is strong enough to be processed by another device, such as a power amplifier or a recording equipment. Preamplifiers are commonly used in audio systems, home theaters, and recording studios to boost the low-level signals from various audio sources, such as microphones, turntables, and musical instruments. By amplifying these weak signals, preamplifiers help to ensure that the audio signal remains clear and free from noise and distortion as it is passed through the rest of the audio system. In addition to amplifying the audio signal, preamplifiers often include features such as equalization, tone control, and volume adjustment, which allow users to fine-tune the sound to their liking.”

Conrad Johnson calls their integrated amps Control Amps.  Basically a power amp with volume, balance , and input selector

My first Integrated Amp in a long time, the Cyrus i7XR also has a DAC .   Integrated Amps have come a long way and some are quite good.

My Dad has a McIntosh 8950 and it is a killer one box solution 

To merge both amplifier,and preamplifier.

myself being an ex Audio dealer  know brands components inside and out 

having spent years upgrading Loudspeakers , and Tech friends that do mods parts quality is far more important then a pretty case . One Huge mistakes people make is in the preamp section , a passive preamp or low quality $25 alps volume pot 

which is a Silver round can up behind the volume pot is a NOT !

it robs detail 100% find a resistive ladder to relay they are the best.