Definitions:
"A REBUILT ENGINE is an engine that has been OVERHAULED using new and used parts to NEW LIMITS by the manufacturer or an entity approved by the manufacturer. At the current time neither Teledyne Continental or Textron Lycoming approve any other entity to REBUILD engines for them. The engine's previous operating history is eradicated and it comes to you with zero hours total time in service, even though the engine may have had used components installed that have many hours of previous operating history . Textron Lycoming uses the term Remanufactured in their advertising and commercial media to describe their factory rebuilt engines. Although this term has no official definition in the eyes of the FAA, when used by the Textron Lycoming and only when used by Textron Lycoming the term Remanufactured should be considered the same as the term REBUILT."
"An OVERHAULED ENGINE is an engine which has been disassembled, cleaned, inspected, repaired as necessary and tested using FAA approved procedures. The engine may be OVERHAULED to NEW LIMITS or SERVICE LIMITS and still be considered a FAA approved OVERHAUL. The engine's previous operating history is maintained and it is returned to you with zero time since major OVERHAUL and a total time since new that is the same as before the OVERHAUL."
So there IS a big difference between an "overhauled engine to new limits" and a "rebuilt/remanufactured engine." The reman/rebuilt is more valuable as it is zero timed and overhauled engines, even overhauled to new limits, are NOT zero timed.