...burn marks on each post. What causes something like this?
Ozone.
A high-voltage spark passing through air breaks down some of the Oxygen molecules (O2), such that they re-combine as ozone (O3). That's why lightning sometimes has that smell. Ozone is highly corrosive; especially on hot metal, like the microscopic point that the spark hits on the cap terminal. That point oxidizes, creating the corrosion you see, and O2. The oxide is not nearly as conductive as the pure metal, so the next spark hits a different spot, causing the crust to eventually grow across the whole terminal. Brass oxidizes to a blackish crust; Aluminum oxide is a lighter gray. In either case, It can simply be scraped or chipped off with a common pocket screwdriver to expose the clean terminal underneath, which will work perfectly for hundreds of thousands more miles.
To reduce the effects of the ozone on the terminals (and to reduce the condensation of water on the distributor cap's plastic), apply silicone grease where this diagram indicates:
(phone app link)
Would y’all recommend replacing the plug wires...?
Only if they fail this test:
(phone app link)