Strictly, off-market means the property is not currently listed for sale on the MLS, the Multiple Listing Service, which is the database agents use to advertise property to each other and to the public portals. If it isn't in there and no agent is representing the seller, it's off-market. That's the whole test.
The loose usage you ran into is real and worth naming. A lot of people say off-market to mean "a deal you got without competing," which stretches to include expired listings, withdrawn listings, and pocket deals an agent is shopping to a short list. An expired listing is genuinely off-market at the moment you call, since the listing agreement ended. It just isn't undiscovered. Forty other investors pulled that same expired list, and the owner has already been told what a retail buyer would pay. So the label is accurate and the implication is misleading.
When you call, that distinction changes your opening. On an expired listing the owner has an anchor price in their head from their old agent, and you're arguing against it. On an owner who never listed, there's no anchor yet, and your job is closer to finding out whether selling is even on their mind.
One thing that trips people up early: your list is not your pipeline. A list of 5,000 records is raw data. What matters is how many of those you can reach and speak to, and reachability depends on the quality of the phone numbers attached, which is usually worse than the sales page implies.