Speaking of HOG Regs, I forgot to mention DIN VS Yoke fittings.
DIN regs can screw into DIN-valve tanks and can be fitted to a Yoke-valve tanks with an adapter.
Yoke regs can only be used on Yoke tanks or tanks with a convertible DIN-Yoke valve.
Another huge can of worms for you to read up about. Plenty of threads discussing this the differences and advantages between the two.
Main differences between regs are Diaphragm/Piston, and a few other add-ons such as Swivel ports, Venturi Switch/Pre-dive Switches and Inhalation dials (or lack thereof).
Swivel ports can make hose routing a bit easier, because your ports aren't in a fixed position.
An Inhalation Dial will allow you to dial down how easy it is to reach your cracking pressure on your second stage. Cracking pressure is the force of inhalation you need to start air flow. A heavy cracking pressure will equate to you heaving to get airflow; not something you want. It is nice to have this dial IMO.
How your second stage works in simple terms is you have a diaphragm(your purge cover) which sits on top of a spring lever which connects to a hardseat, which in turns sits on the opening to your hose.
Breathing in lowers the air pressure in the second stage, flexes the diaphragm/purge cover inward, which lifts the lever and in turn the hard seat which allows air to flow.
Over time this hard seat can indent on the hose opening so much so that you get a premature freeflow that you're unable to stop. Dialing down your inhalation dial when this happens can fix this, saving you the trouble of taking the reg in for early service.
You can also use this dial to prevent a heavy current from free flowing your reg.
Venturi Switches have an on and off position. The On position allows the Venturi effect to take hold and deliver constant air flow when you reach your cracking pressure. With this on you can accidentally bump your reg and cause a free flow. When you have your mouth over it though, the act of you stopping your inhalation will be enough to stop air flow on it's own. Purging the reg or causing back pressure (hand over the mouthpiece or mouthpiece down in the water) will stop the freeflow.
With you flick your Venturi Switch in the Off position, a slide in your second stage will block the Venturi Effect from taking hold and therefore make it less likely for a wave or accidental bump to send your reg into a freeflow. If you breath with this switch in the off position, you should not notice a difference in effort of breathing performance from your reg.
I consider this an unnecessary gimmick because of this, but it has it's uses in certain situations. You usually have this switch set to off until you start your dive (hence Pre-dive Switch).
Not much differences besides that IMO.