amp classification describes the various methods of biasing the output transistors. sometimes the manufacturers take license with their methods and their claims.
class a amps have a single output device with biasing which allows the output to simply amplify the input signal without going through a transition point at a zero output. a class ab amp uses 2 transistors, one for producing the top half of the wave, another for reproducing the bottom half of the wave. the top device is biased so that it cuts off near the zero point and the other device begins to conduct. those ab biased amps produce what is known as crossover notch which produces distortion but they are really the most common audio amplifier arrangement.
you'll never see a true b class bias in an audio amp nor will you ever see a c class, that would be reserved for super high power like for a radar transmitter. class d is one of those "honorary" titles which describes a digital power supply in an audio amp and is one of those big wads of baloney that the audio boyz ginned up.
the floor under a seat is a bad place for an amp for a lot of reasons. start out with the floor pan being subjected to exhaust heat and heat reflected up from a sun baked road surface. also, the seat acts as an insulator and doesn't let heat get away from the amp's case which serves as a heat sink. there's all kinds of trash and fuzz that collects under a seat and there's next to no air flow under there.
ever spill a pop or coffee? it'll run right onto the floor. floors seem to always catch whatever liquid, rain, etc. if i were you, i'd find a better spot to mount an amp.