The RB211 524G and H are the same engine, the difference in power achieved by pin programming of the FAFC.
58000 lbs and 60600lbs thrust respectively.
The 524G/T and H/T have exactly the same thrust levels as above but the improvements in emmisions (and sfc) come from the 04 module which is from the Trent family of engines.
The 04 module (hp compressor, combustion chamber and hp turbine) improvements come from basically the blade aerodynamics, comp. and turb. plus the redesign of the combustor. The HPT also has design improvements to the blade shroud interlocks which are more robust..as anybody who does boroscopes could attest too!
An aircraft can have a mix of 524G and 524G/T or 524H and 524H/T, the only way to tell the difference in operation is on start up where the acceleration profile to idle differs slightly.