Amp level versus line level inputs for subwoofers

I'm trying to learn something about subwoofers and have noticed that some subwoofers have a choice of input type. Could someone please explain the difference between these two types of inputs and the relative advantages and disadvantages of each?

Basically, I think a sub with both types of inputs can receive its signal from either the system's preamp or its amp. I assume that if the signal comes from one amp or mono amps, the sub would then retain more of the sonic characteristic of the main amplifier and less from its own internal amplifier.