Depending on who built it and if any shortcuts were taken, a rebuilt engine may have a shorter life than remanufactured units but the costs can sometimes be much less especially on the higher priced engines.
The rebuilding process is typically performed in a local shop. Each job is handled differently and depends upon the judgment and skill of the individual mechanic. Parts believed to be serviceable, are inspected, cleaned and reused to the maximum extent possible. Only worn or broken parts are actually replaced, unless stated otherwise.
Remanufacturing is a factory process. It starts with a sound, undamaged engine core that is carefully cleaned, conditioned and machined to OEM tolerance specifications. All wearable components are systematically replaced with new parts including but not limited to pistons, piston rings, valves, lifters, etc. Remanufacturing is similar to building a new engine including standardized procedures, quality controls and final factory testing before shipment.