The term engine is because of that early lathes were driven by steam engine. It consists of basic parts like bed, head-stock and tail stock but head-stock is more robust and has additional drive mechanism for multiple speeds. Engine lathe can feed cutting tool both in cross and longitudinal directions with the help of carriage, feed rod, and lead screw.
Belt drive lathe gets power from an over head line shaft equipped with speed cone and one or more back gears. Individual motor driven lathe gets power from individual motor.A geared head lathe gets its power from constant speed motor and all speed changes are obtained by shifting various gears located in the headstock.