The important distinction is what the token does. In a tokenised register, the token is the record of ownership and the administration workflow runs on the ledger; investors do not hold or trade the tokens themselves. In a publicly tradable tokenised fund, tokens can be transferred between wallets or traded on venues, which raises transfer-restriction, eligibility and secondary-market questions that most professional-investor funds cannot accept.
The operational benefit of a tokenised register is that the register, the dealing engine and the NAV share one source of truth, which removes the reconciliation step between them.