When it first showed up in the early thirteenth century, gold was just an adjective, not a name of a metal. It didn’t get attached to the metal of that color for another two centuries. The word “gold” comes from the Old English gold, which evolved from the Proto Germanic gulth and further back, the Proto Indo European ghel, which means yellow/green (in fact, in my colors post I mentioned that ghel is the origin word for yellow). In other words, gold is basically saying “that metal that’s yellow”.
Silver comes from the Old English seolfor and Mercian sylfur, which meant silver or money. In Proto Germanic the word is silubra, but from there it’s uncertain because Proto Indo European bequeathed arg- (shine, white) which gave us the Latin argentum and even the word argent here in Modern English. Silver jumped in over a thousand years ago (possibly of Asian extraction) and just stayed and now we use it to describe the shining white metal.
Tin comes from the Old English tin (I’ll never be able to pronounce that!) and Proto Germanic tinom. There’s nothing further back than that as Latin uses a completely different word, stannum. Most European countries use variations of both the Latin and Proto Germanic for tin to differentiate between the raw form of the metal and the plate form of it.
Unlike the other words here, platinum first showed up as a metal, and relatively recently in 1812. Its name comes from Latin, of course, but that was from the Spanish word platina or plata, which means silver. Apparently when it was first discovered, it was thought of as a lesser form of silver.
Or “aluminium”, for you UK types. It’s another one that didn’t show up until 1812. Its oxide form “alumina”, actually came first, and was named from the classical Latin alumen, which means alum, a salt used in medicine, tanning and dyeing among other things.
Tony Jebson’s page on the Origins of Old EnglishOrbis Latinus