Web3Provider.getSigner().signMessage() vs Wallet.signMessage()

[fauxbytes]

Hi.
A message signature can be obtained in the browser:

const provider = new ethers.BrowserProvider(window.ethereum);
const signer = provider.getSigner();
const signature = await signer.signMessage(message);

In node:

const wallet = new Wallet(priv, provider);
const signature = await wallet.signMessage(message);

Assuming the use of the same account, same input message - will those two yield identical signatures?
If not, how do you get identical signatures across browser/node?
If yes, could you please elaborate? the two independent implementations (JsonRpcSigner.signMessage and Wallet.signMessage) seem quite different.
Thanks.

[ricmoo]

Yes, assuming both implementations follow RFC 6979, (which all modern implementation do) the same private key will generate the same signature for the same message.

A JsonRpcSigner sends the message to an another location (e.g. a geth node, with a Go implementation of ECC signing) to be signed, so it’s implementation is like just serializing and sending it over a wire.

But the ECC algorithm and related maths are all the same under the hood. :)

[fauxbytes]

Many thanks.
Don't suppose you could suggest a method to test this in node (I am confident the answer is correct. Just keen to see it in the works :E)?