Before I answer this, let me tell you a little bit about myself. I'm an EE, and I primarily work in the Pro-Audio industry-- although I have also done some work for an audiophile company. I've been using pro-audio equipment for 25 years, and designing pro audio-stuff for 14 years. I mention this so that you can judge for yourself the quality of the answer I'm about to give you.
First, what @Rob said is correct in that the term "HiFi" does not have much meaning. So I am going to slightly reword your question to this:
What is the difference between consumer audio and professional audio?
Before answering this, let me point out that pro-audio is not just what you would hear at a concert or what a wedding DJ would use. Pro-audio gear is used at an airport for their paging system, or at a restaurant for their background music, or in a boardroom, or at a movie theater.
There are many differences, and I'll highlight some of them:
Pro-audio has a different purpose that home audio does not always need. Homes rarely need an amplifier that can drive 100 speakers in parallel. They rarely need an amplifier that can drive 8,000 watts. Homes tend to switch from one audio source to another, not mix several sources together.
The connectors used are different. Amplifiers that are used for DJ's, touring concerts, etc. tend to have Neutrix Speakon connectors. Amps used for "installed sound" have screw-terminals or Phoenix terminal strips. Consumer amps tend to have screw terminals or some light-weight wire clip things. Consumer equipment uses (typically) unbalanced audio signals on RCA connectors while pro-audio tends to use balanced signals on XLR connectors.
There are literally thousands of other differences that are dictated by the intended purpose of the equipment.
Pro-equipment tends to be more rugged. Especially the equipment that is intended to be used in a live or touring sound environment. They use connectors that can withstand a lot of mate/unmate cycles. The chassis are made from thicker sheet metal. The chassis are designed to be bolted into an equipment rack. Typically the equipment has been designed to withstand more shock, vibration, and temperature extremes. Some of it has been made with withstand rain, direct sunshine, fog-machine condensate, and even salt spray.
Yes, pro-audio amps tend to be higher power than consumer amps. Also, the stated specs of a pro-audio amp tend to be more "real" than the stated specs of a consumer amp. When rating the power of an amp there are a lot of ways that the specs can be fudged, and pro audio amps tend to fudge them less or if they are fudged then there is usually a footnote in the manual that explains exactly how the spec is measured.
This gets even worse when you consider car audio amps. The max power for a car amp is usually rated at 10% THD+Noise. Basically they crank up the power until the output is 10% THD+N and that is the spec that they quote. Home amps tend to spec the noise at 1% THD+N. Pro amps tend to go to 0.1% or 0.05% THD+N. Of course, there will be companies that do not follow these generalizations.
Pro-audio gear tends to be built to last. There are pro audio amps that are still running strong after 20 years of solid use. Consumer audio gear, not so much. Part of this is because pro gear is used in more hostile environments, but the other part is just liability. Imagine this, your amplifiers are powering a large concert with 50,000 people in the audience. 5 minutes before the concert an amplifier dies and happens to destroy a bunch of speakers in the process. The concert is canceled and tickets are refunded-- then the lawsuits start. Something like this could end up costing someone $1million or more.
This is one reason why pro gear is more expensive. Better components cost more. For example, decoupling caps on a +15v rail might be rated for +16v in consumer gear. But in pro audio gear they would probably use 25v or even 50v caps.
Levels & impedance
Pro-gear is usually designed to handle a wide range of signal levels. Some mic signals are only 2 mV p-p, while other gear might be spitting out 30v p-p. This is a huge variation. Of course not all equipment is designed to take in the entire range of signals, but pro gear in general can handle the wider range much better than consumer gear.
You mention impedance, but this is largely a non-issue. Old-school equipment was designed to use 600 ohm impedance signals. Modern equipment, both consumer and pro, have low impedance outputs driving high-impedance inputs. This is on the "line level" signals, of course.
For amplifiers, most consumer and pro gear can handle 4 and 8 ohm speaker impedances. Some, but not all, pro audio amps can handle 2 ohm speakers as well.
I should also mention +48v Phantom Power. Consumer gear doesn't provide this at all, while it is standard for pro gear that needs to connect to microphones. But more importantly, most outputs on pro-audio gear is designed to plug into inputs that are providing Phantom power. Consumer gear cannot withstand the +48 volts, and could be damaged if connected to a device that is providing phantom power.
Mixing Consumer and Pro Gear
There is a lot of mis-information about mixing pro and consumer gear. With a few exceptions, you can mix them just fine. The exceptions are: Phantom Power and Signal Level. As mentioned earlier, with Phantom power you can destroy gear. If the signal levels are wrong you will just get very quiet or very distorted sound but no damage.
So, go for it! Just be careful about Phantom power and you'll be fine. It might not sound as good as it could, but it will work.
Some of the mis-information that I've heard has to do with the pro-gear producing sounds (transients, etc.) that are too hard on the consumer gear. This is complete nonsense. If it is doing that, then it will sound distorted and you know to turn it down. That's all.
What I wrote above is a large generalization. There are exceptions to everything. There is consumer gear that is well made, with low noise, etc. There is also "pro" gear that is terrible. And, of course, there are "crossover" products that have features of both pro and consumer gear. As with everything, your mileage (kilometerage?) may vary.