The 340-200 and -300 all variants are only powered by CFM International CFM56-5C engines.
The A340-313X, which was previously referred to by SQ
as the 343E, are higher-gross-weight frames with a a centerline fuel tank, strengthened wing, and the tail enhancements from the A330-200.
The A340-314, A340-314X, or whatever, the new A340-300 Enhanced, are powered by the new CFM56-5C/P. They include a completely new and updated avionics suite with LCD
displays, a new FBW system with additional FBW controls for the rudder and some other basic improvements from the A340-500/600 family.