You have to be careful not to put too much weight on this classification. A lot of it is either marketing or good old-fashioned snobbery. Most people who say pro gear has no place in the home haven’t actually listened to it in a home setup. A lot of times, something marketed as pro will sound just as good as the audiophile gear, it’ll just look more aggressive (some would say uglier), be built tougher, weigh less, and have a much smaller profit mark up.
Some practical items that I can think of that come up with “pro” amps like the Crown XLS series: fans and input voltage. All have built in fans. This is great because it keeps them cool even when they’re being pushed hard for hours at a time. Not a problem because that’s what they’re designed to do. However, audiophiles think “fan” and run for the hills. They don’t want to hear a fan whirring along, messing up the sound of the music. But those that have used these know that you can’t hear the fan so it’s not an issue. Now onto input voltage. This is usually 1.4 volts in the pro world. So the the original line of Crown XLS amps (1000, 1500, 2000, and 2500 models) ran on 1.4 volts into the XLR inputs. So if you were running a home balanced setup with XLRs you were getting full rated power out of the amp. But everyone else who ran RCAs (more common in the home audio world) were running at .775 volts and therefore the amp wouldn’t make full power. Depending on your setup, you might not get enough volume out of the amp, even though it was rated for huge power. I personally never had a problem with it though. I always got plenty of power for my needs, even using the RCAs.
Eventually Crown caught on and found out that audiophiles were buying their pro amps and using them at home, so they made some design changes to their new line. First they made the face look more subdued and added an option to turn off the running lights, making it more appealing to the home market. In addition, they offered an input sensitivity option. Now you can change it to “high” sensitivity to get full power out of the RCA inputs. It still has the fan, but again, it’s inaudible with music playing, so no big deal.
So this is a good example of pro gear potentially having practical issues, but mostly being perfectly acceptable for anyone that cares more about sound than reputation.