I don't think so.
Segwit is simply a different payment script + adress format, it does not generate a different key. A private key can both generate a traditional adress (P2PKH), or a segwit one, (P2SH).
This answer is a bit more indepth about it,
https://bitcoin.stackexchange.com/a/70123This is correct.
Addresses are derived from public keys, which are first derived from private keys.
Private key -> public key -> address
So you can have one (WIF) private key, with different addresses, depending on the private keys.
Ordinarily you can create 2 P2PKH addresses from one private key, by using either compressed or uncompressed public keys.
You can also derive P2PWKH, P2SH, and P2SH-P2WPKH addresses from the same public key (note that segwit addresses are all derived from
compressed public keys)