Ah, cost is the amount to produce and price is the amount to consume then? I never actively tagged those ideas with distinct words, but I appreciate the insight.
Using "cost" to refer to the amount you pay for something and "price" for the amount you get for selling it is pretty standard usage, especially in accounting contexts.
Cost is on the producers side, peice is whatever the product can be sold for. Value is depending on circumstances, accounting value on the other hand is pretty well defined, and either based on cost (inventory at the manufacturer) or purchasing price (inventory and assets on customer side).
I think the term cost can only be specified with respect to an entity.
A given good has multiple cost, up and down the supply chain. A widget can have different costs to the original manufacturer, the wholesaler, retailer, and finally consumer.
It makes no sense to say the cost of a widget is X, without specifying cost to whom.