A rebuilt engine is an engine that has inspected and had any broken or damaged parts replaced. These replacement parts could be new or used. Any parts that are within wear limits are kept.
A remanufactured engine is one that has been cleaned, inspected, and brought as close to factory specs as possible. Any wearable parts are replaced with new parts or used parts that have been inspected and meet factory specs.
One major advantage of a remanufacture is that parts with heat stress, hairline cracks, or any other wear not caught during the inspection process or deemed to be within wear limits may not be replaced, leading to them failing later on.