So if I understand correctly you can use the same seed to generate different public and private keys for each coin.
Well... you can see from my previous post that the same seed actually generated the same private keys and the same public keys... it is just the addresses derived from the public keys that are different... as they use different formats/hash functions/algorithms etc for converting from a public key to an address.remember: PrivKey -> PubKey -> Address.
Also, by using different "derivation paths" you can generate different private keys from the same seed... this is why each coin tends to use a unique derivation path, so you can have different keys for each coin. That is how popular hardware wallets like the Trezor and Ledger wallets work... one seed -> different derivation paths for each coin -> different private keys -> different addresses... it is also why they hardware wallet devs have been able to create the "fork coin split" tools... by creating a forkcoin wallet (ie. BitcoinCash) with the same derivation path as the original coin (ie. Bitcoin), you can easily access your BitcoinCash as it generates the same private keys etc.
Can we generate the same private key for both coins with the different public address, is this option is doable?
Obviously, because that is exactly what I did... At the end of the day... a "private key" is just a (very) large number... so you should be able to put that same number into any given cryptocurrency that uses "numerical" private keys and it should then be able to be converted into a public key and from that public key, it should be able to derive an address.
