It's the same public key and it's the same Schnorr signature. Frost is not generating a new keypair in any sense.
Alright … now I’m just getting familiar with frost … but it looks to me like the bifrost implementation generates a unique (group_pk) pubkey for each “group” of “shares”… and it isn’t straight forward how the “main” pubkey would be obtained by a client “signer”, signing with one of the “shares”. What do you know about this?
https://github.com/FROSTR-ORG/bifrost/blob/master/src/types/group.ts#L24
Discussion
Basically "group_pk" is not generated, it's detected. And the thing being detected there is your actual nostr npub in hex format (provided the shares are of splits of your nsec).