From a distance they look similar but the Model C was designed for adding Imperial measurements and has a dial that goes up to 11 for adding inches. Both models feature a dial for fractions on the far right, where Model Bs only have decimal dials. All models have a ruler on top.
My Model A came with the original case, which was designed with a notch cut in the side so you can access the stylus storage and the clearing lever without removing it from the case. It also came with the original instructions!
To add, put the stylus in the dial for the corresponding digit using the larger numbers, and turn clockwise until the dial stops. The mechanism automatically carries the one without having to move in different directions like with a "shepherd's hook" design. Here is 31337 + 4.
To multiply, perform repeated addition and shift left for each term in the multiplier. Here is 12 x 12.
You can also perform division using the repeated subtraction method but you have to keep track of the number of subtractions in your head. To clear the registers, just pull on the lever on the right side. This also ejects the stylus for you if it's in storage.
As I mentioned the Model C was designed for Imperial measurements and had a dial that went up to 11 so inches could carry over into feet. Here I'm calculating 2' 9 3/4" + 1' 6 7/8". Doing math with Imperial measurements really makes you appreciate the Metric system.
Due to the size and the case design, I suspect Addometers were mostly stored on or in desks and pulled out for quick arithmetic and they work well for that. The Imperial model I have was probably thrown in a toolbox and has lots of wear and even initials carved in it.