Is there a difference in the drive shape in that the impact has a different drive to which the sockets are shaped so they are not interchangeable with regular ratchet/breaker bar drive? Or is the drive the same on both but the difference is purely in the torque range?
The difference is in torque (twisting capability)
Impact wrenches are designed to output higher torque than ratchets.
In the linked products, the impact wrench churns out 180 lb-ft while the air ratchet gives just 70 lb-ft in comparison.
An easy example that can illustrate the difference is a wheel lug nut.
When undoing wheel nuts by hand, you will find that increasing lever length makes it easier to undo the nut. It is quite possible that a regular wheel wrench will bend before the nut budges.
An impact wrench will have a better prospect of cracking the nut loose by virtue of its higher torque.
Air ratchets are useful for loosening/tightening multitudes of low-to-medium torque bolts. You don't want to use an impact wrench here because it can easily over-torque the bolts and cause damage to the threads or snap off the bolt heads or studs.
There is a fundamental difference between an impact wrench and an air ratchet wrench in how they operate.
An air ratchet wrench is the easiest to understand. Inside there is a vane motor. When air is directed into the vane motor it will spin a little gear box making a back and forth action. This back and forth action is directed into the socket drive via the direction selector. Without applying air an air ratchet wrench is just like any other non air ratchet wrench. Normally you break a fastener loose by hand and then pull the lever to apply the air to back it all the way out. The air wrench is able to apply a semistable amount of continuous torque.
An impact wrench also has a vane motor. Between the vane motor and the socket drive there is a special set of hammers that operate in two modes. The first mode is if the socket is held stationary like on a tight bolt. In this mode the vane motor, very quickly, spins up the hammers and they impact the output drive. This hammering action can occur as fast as 20 to 40 impacts a second and can generate tremendous amounts of torque. My Ingersoll Rand 2135 impact is rated for 1000 foot pounds. That torque is only achieved at the instant of the hammer strike and is not continuous. The second mode is if there is no or very little resistance on the socket drive. In this case the hammers stay locked and the impact smoothly spins the fastener.
Both types or wrenches come in 1/4 in, 3/8 in, and 1/2 in drives. Impacts also come in a 3/4 in drive and 1 in drive.
The difference between the two is not just torque it is the desired application as well. If you want to loosen something very tight or with a sudden shock then an impact is your tool. If you want to tighten something very tight and it's big enough that your not afraid to snap it off then and impact is your tool. If space is limited and something is not very tight then an air wrench may be your choice. I've seen people take something apart with an impact an put it back together with and air wrench.
One final note, an impact translates little to no torque to the end user. Just support the weight and hold it steady. The air wrench translates ALL to torque to the end user and it is up to the user to hold it steady. Be prepared when pressing the lever/button on the air wrench. If you are not prepared busted knuckles or hilarity will ensue.