Car audio- and car stereo amplifier are two longer terms meaning the same.
Most car amplifiers are 2 or 4-channel. The sound environments in a car can be different and the only way to overcome noise and sounds from outside is to increase the sound with more amplifier power or the fidelity as with a car equalizer. Don't expect a car amplifier to perform more clean audio than half of its rated output power.
Class D amplifiers have been more developed and common since they provide more power vs size and weight. Subwoofers also demand more power. There are also powered subwoofers where the amplifier and subwoofer is integrated.
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