are “all” metal wallets functionally equivalent?

Within the context of wallets, is it correct that a metal bitcoin wallet needs to store both public and private keys?

I’m looking at some metal wallets and want to clarify that the’re all basically the same in that they’ll give you different bits and bobs which are then must be physically arranged?

Or, are some metal wallets etched or otherwise “written” and then sent to the user? Because that seems a very trusting act, to provide a private key to some third party.

Just dealing with bitcoin. Perhaps naively thinking of storing public/private key “written” down with metal.

I would think something like:

minting physical bitcoins

would the point of such a wallet. Obviously not minted, but just storing the public/private key on metal for reference.