Copper and iron pass through two different forms: an ore you gather and an ingot you process. Recipes for tools and benches commonly ask for the ingot, so carrying an ore stack does not yet satisfy that ingredient.
Find the ore-bearing block
The stone variants below have generation references across several regions. Their maps are a starting point for choosing a destination. Other host-rock variants have their own records, so the name of the embedded rock matters.
Process at a Furnace
The observed recipes process one matching ore into one ingot. Copper lists 10 seconds and iron lists 14 seconds. These are recipe processing times, not a measurement of an entire gathering trip or a promise about a modded server's throughput.
Decide where the first ingots go
The Blacksmith's Anvil and Armorer's Workbench each use copper in their station recipe. Iron is also needed by the Repair Kit and the initial backpack unlock. Check workstations before spending the last of a material on equipment, and follow Crafting an Iron Sword once the weapon station and ingredients are ready.