The LS device requires more current to operate, has TTL thresholds(0.8V and 2.4V IIRC). The output drive should be 10 LS loads or at least 4 mA, but LS outputs cannot source very much current.
The HCT device, requires a fraction of the current required by it's LS counterpart, has TTL thresholds(0.8V and 2.4V IIRC), and has an output driver which can sink or source 6 mA.
The HC device will take a bit less current then the HCT, has CMOS thresholds (Vcc/2), and has an output driver which can sink or source 6 mA.