It isn't. "Overhaul" does not require taking it to new limits, only "rebuilt" does. "Overhaul" need only take it to the limits specified in the manufacturer's overhaul manual, which may not be the same as new limits, and I believe are usually if not always tighter than "service limits," which are the limits to which a component may be worn before it must be removed from service.
The crank doesn't have to be replaced with a new one in order to call it "rebuilt" if the old crank is still, or can be restored to, new limits. OTOH, there are certain parts which the overhauler may replace with new regardless of the condition of the old parts, e.g., a Lycoming factory "overhaul" always includes new cyinder assemblies even though that is not required by either the FAA or Lycoming's engine overhaul manuals.
At the end of the day, it all comes down to a careful examination of the description of the work to be done provided before the job, and the documentation accompanying the engine back from the shop where the work was done. However, to answer your question as directly as possible, Lycoming charges about a 15% premium for a "rebuilt" engine over an "overhauled" engine, and the fact that the difference is what it is tells you what the market seems to think the difference is worth.