A blockchain is a distributed non trustful database with a method for resolving disputes built in. Roughly speaking in something like quorum, everyone checks everyone else's work, and the majority consensus is ground truth. DTCC requires a trusted third party to administer the database. Quorum doesn't. Quorum could presumably also replace intra-bank transactions as well (instead of maintaining some other kind of database).

I guess the missing piece that seems to break people's brains; the ledger in the distributed database represents a dollar amount (in the case of quorum's dollar thing) and it has money-like rules, unlike, say, postgres which ultimately relies on some other piece of software to make ledger like transactions.