Lycoming has THREE engine classifications.
A new engine is just that. All new parts that all meet new specifications and tolerances.
A "rebuilt" engine is a used engine rebuilt to new engine specs and tolerances.
An "overhauled" engine is a used engine overhauled to within service limits.
Lycoming does all three, but they also say this:
Your independent engine shop cannot legally call their engines "rebuilt" because of that. They're just overhaulers.
Here's an excerpt from the Lyc overhaul manual:
For instance, for the A-B engines, the tappet body outside diameter, when new, is between .6232" and .6240". A tappet being reused cannot be smaller than .6229" (the service limit). The rebuilt engine's tappets will be within the new specs (and most likely Lycoming will just use new tappets) and an overhauled engine can have the tappets worn as small as .6229".
So, a used .6229" OD tappet is as much as .0011" smaller than the largest new tappet. Sounds bad? Consider that a human hair is about .003" in diameter, nearly three times that .0011" difference. We are talking very small tolerances here. It's .0003" smaller than the smallest new tappet, a tolerance ten times smaller than that human hair.
I bought a lot of Lycoming overhauled engines. Most of them had recycled cases, some had recycled cranks and rods. Everything else was new. Everything they use gets NDI, Non-Destructive Inspection, of various types including eddy current, magnaflux, dye-penetrant and so on. Even new parts get the NDI< since one has to catch voids (bubbles in castings) and cold shuts (where the aluminum flowing into the mold gets bit too cool and when the leading edges meet at the far end of the mold, they fail to fuse together completely. The casting looks good but is weak. Eddy current catches that, since that poor joint won't carry the eddy current properly across the unfused area and an anomaly in the generated magnetic field triggers the eddy current failure detector.
Once in a while we received a zero-time rebuilt engine rather than the overhauled we asked for. They were probably short of serviceable cores for overhaul. I even got a brand-new engine once, for overhauled price. No useable cores at all, probably.