The difference is that the motor assemble has either one or two voice coils rated at either 2 or 4 ohm.
Your amp does not have to be "dual" is you have a DVC sub.
Basically is you have a DVC sub, it gives you wiring options. For example if you have a 1- 2ohm DVC sub, you could wire it in series to 4ohms or you could wire it in parallel to produce a 1 ohm load to your amp. Same applies with 4ohm DVC, except it would be 8ohm and 2 ohm respectively.