I'm going to give this one a shot. A little less info than the link from the first post, but a little more than we've got so far. I'm not an expert, so please feel free to give any corrections you see.
The gas systems job during firing is to use enough pressurized gas from the barrel to push the BCG hard enough for the action to go through its cycle. Too little push, and its under-gassed, commonly causing short strokes. Too much push and it's over-gassed, which is harder on the rifle, rifleman, and on the brass.
At the chamber, the pressure of the gas behind the bullet is highest. As the bullet travels down the barrel the pressure gradually drops, until the bullet leaves the muzzle which allows the pressure to rapidly lower (uncork).
The gasses start venting into the gas system once the bullet passes the Gas Port. So the pressurized gas is pushing out the port, through the gas block, into the gas tube, and back against the bolt carrier key. The duration of the time when these forces are exerted (from when the bullet passes the gas port and when the bullet exits the muzzle) is called Dwell Time (when the high pressure gas is dwelling in the gas system). The force needed to cycle the action properly is a function of the Gas Pressure and the Dwell Time. (Another wrinkle is that we can increase the Port Size for any given gas system length, which will allow more gas through, but I don't want to confuse things much here.) A port closer to the chamber has higher pressure gas, so it needs less dwell time to have enough force to cycle the action. Conversely, a port farther down the barrel has lower pressure gasses, so it needs a longer dwell time to cycle the action.
On a 20" barrel with Rifle Length system, the gas starts venting into the port somewhere around 13" down the barrel. This means the dwell time is roughly during the last 7" the bullet travels through the barrel.
On the original Carbine Length systems (which I think had either 10.5" or 11.5" barrels) the gas port is a little less than 8" through the barrel. So the dwell time is only during the last 4"-ish (depending on 10.5 or 11.5) of the barrel. Because the gas port is closer to the chamber, the gas pressure is higher, so it needs less dwell time.
On the military's M-4, the 14.5" barrel worked with the Carbine gas, but not with the Rifle Length gas, so that's what Uncle Sam went with. For a civilian 16" barrel, we realized that even though the Carbine gas still worked, it was a little over gassed sometimes. So the Mid-length Gas system was born.
On a 16" Mid-Length gas system, the port is almost 10" down the barrel, so the dwell time is that last 6". Some folks find the recoil of a Mid-Length 16" AR better than a similar Carbine gassed one. Some folks prefer the aesthetics of the MidLength, because the longer handguard makes the rifle look more appealing (or the bayonet lug is at the right spot).
I think that is a rough primer on the mechanics and differences in the gas systems.