The physical market is where cargoes change hands. A refiner buys crude from a producer or a trader, agrees a grade, a loading window and a delivery point, and takes the barrels. The unit of trade is a cargo, which for crude is typically 500,000 to 2,000,000 barrels depending on the vessel. The terms are bilateral and largely private: there is no exchange, no central order book, and no obligation on either party to tell anyone what they paid.
The paper market is standardised contracts on the same commodity, traded on an exchange, and usually closed out before anything is delivered. Everything except price is fixed in advance by the exchange, which is what makes the contracts interchangeable and therefore liquid. Most quoted prices come from paper, because that is where volume concentrates: the front-month WTI contract alone turns over many times world daily production every day.
That last figure is often quoted as though it were evidence of something wrong. It is not. A hedge has to be entered and exited, a market maker turns over inventory continuously, and a spread trade is two contracts rather than one. High paper volume relative to physical is what a liquid market looks like, not a distortion of one.
Delivery is what ties the layers together. A futures contract that can be settled with physical barrels cannot drift far from the physical price near expiry, because anyone could buy the cheap one and deliver into the expensive one. That arbitrage does not have to be executed often to work; the credible threat of it is enough. This is why the mechanics of a contract's delivery specification matter even to a trader who never intends to deliver.
Not every contract works that way. Brent settles financially against an index of physical assessments rather than by physical delivery, so its link to the physical market runs through the assessment process instead of through a delivery threat. Both mechanisms work; they fail differently, which is worth knowing before trusting either near expiry.
Physical trade itself rarely prices outright. A cargo is agreed as a differential to a benchmark, so a deal struck weeks before loading does not require either side to take a view on the flat price. That separation, between the level of oil and the value of this particular oil, is the single most useful idea in the physical market.