Carry is the total cost of holding a barrel from one date to another. It has three components, and all three are observable rather than estimated: the rent on the tank, the insurance on the contents, and the interest on the capital the barrel represents.
Carry is what turns the forward curve from an opinion into a constrained object. The gap between two months is bounded above by full carry, because a wider gap is a riskless trade for anyone who can rent a tank. That is the argument in contango, and it is the reason the upside of a calendar spread is capped while the downside is not.
The financing term is the one people forget, and it is the reason curve structure moves when nothing physical has changed. A rise in short rates raises the cost of carrying a barrel, which widens the contango a market can sustain. The curve got steeper and no tank moved. This matters for any relationship you try to fit between structure and fundamentals: rates are a live input, and omitting them attributes their effect to whatever else you did include.
Storage capacity is not a single number either. There is tankage at the delivery point, tankage in the wider region, and there is floating storage, each with its own cost and each available at a different point in the curve. The market works down that ladder: cheap local tanks first, then regional, then ships. The steepness of the contango at any moment tells you roughly which rung is being bid for.