They measure two entirely different kinds of damage, and a buyer who treats them as interchangeable freshness indicators will eventually accept a cargo that should have been rejected.
Acid value counts free fatty acids, expressed as the milligrams of potassium hydroxide needed to neutralise one gram of oil. Free fatty acids come from hydrolysis: water and enzymes splitting fatty acids off the triglyceride backbone. Most of that happens before and during refining, in damaged or badly stored seed and in the crude oil, and neutralisation is the refining step that removes it. So the acid value reports on seed quality, crude storage and how well the refinery did its job. Under the Codex standard for named vegetable oils a refined oil should be at not more than 0.6 mg KOH per gram; the same figure expressed as free fatty acids is around 0.3 per cent as oleic acid, and it is worth agreeing which convention the certificate uses.
Peroxide value counts primary oxidation products, expressed in milliequivalents of active oxygen per kilogram. Peroxides come from oxidation: oxygen attacking the unsaturated fatty acid chains, accelerated by heat, light and trace metals such as iron and copper. Most of that happens after refining, in storage and during the voyage. The Codex limit for a refined oil is not more than 10 milliequivalents per kilogram.
So one parameter looks backwards at the seed and the refinery, and the other looks at what has happened since. A cargo can pass one and fail the other, which is why both belong in the contract and why both should be re-tested at discharge rather than accepted on the loading certificate.
One refinement worth knowing: peroxides are intermediates, and they decompose into secondary products. An oil that has oxidised badly and then sat for a while can return a deceptively low peroxide value. If you are protecting a long shelf life, ask for an anisidine value as well, which measures those secondary products and therefore reports the oxidation history rather than only the present state.