Question
Is there a difference between the copper & iron, silver & gold backpacks? If not, are any differences planned?

Nope, and nope.
Copper & iron backpacks, and silver & gold backpacks are meant to be the same, so the player can choose what resources they want to use.

That said, did you have anything in mind that could differentiate them?

Maybe for gold & silver, one could be able to auto-pickup items and the other could resupply items in the hotbar? Either of them using either a configurable filter (with a toggle for a whitelist or blacklist) or just going by what's already in the backpack. Then for the later tiers, both abilities could be present.

I would rather add those abilities as upgrades and give each backpack a certain number of upgrade slots.

Now that I think of it, the copper and silver backpack aren't enable by default. Only if another mod adds copper or silver ingots the backpack for it will be enabled, so having a feature just for those backpacks excludes a lot of players from being able to use it.