Industry terms are used loosely, indeed, but I won't get into that! It's simply buyer beware!
New limits and serviceable limits are two different things in most cases. A certain amount of wear can be tolerated on most engine components, and these are known as serviceable limits. An engine can be disassembled and inspected, and even if wear is found, it can legally be reassembled and returned to service, as long as none of the worn components exceed serviceable limits. This could never legally be called an overhaul, even though all new consumables are (usually) used. All times keep accumalating uninterupted since the last real overhaul. the real problem is that parts that were barely within limits at the time of the inspection, are now surely worn beyond limits after 600 more hours! The engine still runs, and is worth core value, but that's probably about all that's good about it!
I have never understood the mentality of not properly overhauling a high time engine that is already disassembled.
I wonder what else they scrimped on?
While I agree with most of what Carl says above, you can have a legal overhaul of an engine to serviceable limits which resets the TSMOH clock. The chances of you going the full TBO is pretty slim but some parts have service limits that include quite a margin for safety, mom, and apple pie. The manufacturer specifies what parts have to be replaced, reworked, or just checked for service limits during an overhaul. Carl is right that just tearing down an engine and checking service limits and then reassembling does not count as an overhaul unless the entire list of things are done that the manufacturer specifies.