Centralized exchange wallet is the same as centralized exchange. The wallet owned by the exchange to custody the coins of their users are referred to as centralized exchange wallet. It is not a noncustodial wallet developed by the exchange. If a wallet is developed by an exchange and it supports seed phrase, it is referred to as noncustodial wallet just like other noncustodial wallets. All of them that I know are close source which also makes them not recommendable.
The centralized exchange does not need to develop their own non custodial wallet because there are open source non custodial wallets that are available and reproducible by centralized exchanges.
They don't deploy non custodial wallet from open source code for users because they want to fully control user funds. It is main reason, not because lack of available reproducible wallets or resources for development of their own wallets.