A full cord, a face cord, and the units that are not units at all
A full cord is a precisely defined quantity: a stack measuring 4 ft high by 8 ft long by 4 ft deep, which is 128 cubic feet of neatly stacked wood and air. That definition is written into weights-and-measures law in most US states and Canadian provinces, and it is the only firewood unit you can safely compare prices against. The arithmetic is simple — multiply stack length by stack height by the piece length in feet, then divide by 128. Note that the 128 ft³ includes the gaps between pieces, so a cord is not 128 ft³ of solid wood; the solid content of a stacked cord is well under that, which is normal and expected.
A face cord (also called a rick or a run) is the part that catches buyers out. It is 4 ft high by 8 ft long, the same face area as a full cord, but only as deep as the pieces are long. So a face cord of 16 in wood is one third of a full cord, a face cord of 12 in wood is one quarter, and a face cord of 24 in wood is half. Two sellers can both advertise a face cord for the same price and one can be delivering fifty percent more wood than the other. Whenever you see a face cord price, convert it to a per-full-cord price before comparing: multiply by 12 and divide by the piece length in inches.
Then there are the terms with no legal definition at all. A truckload, a load, a pile, a bush cord in some regions, or a price quoted "per pickup" tells you nothing about volume, because pickup beds differ wildly and a heaped load is mostly air. The defence is to insist on delivery stacked, or to stack it yourself before paying if you can, then measure length, height and piece length and check the result against what you were sold. Also ask about seasoning: green wood can be roughly half water by weight, burns poorly, produces far less usable heat and deposits creosote in the flue, so wood bought by volume is only a bargain if it is genuinely dry.
Volume estimates assume neatly stacked wood with pieces running the full depth. Loosely thrown, round, or irregular wood occupies more space for the same amount of fuel. Firewood is legally sold by the cord or fraction of a cord in most jurisdictions — check your local weights and measures rules if a seller will only quote in non-standard units, and have any wood-burning appliance and chimney inspected and swept regularly.