A high current Class AB amp has a decent sized power supply to help a good strong output section pass more current to your speakers at lower impedance (ohms) loads. A regular non-high current design class AB amplifier has a weeny power supply just good enough to provide current and voltage to a higher working voltage output section that will never see (never recommended to see anyway) lower than around 4 ohms impedance.
Basically, it's more rugged, and will produce more power at lower impedances if it is a "High Current" amplifier.