Think of it like going into a bank and getting them to write a bankers draft from your account. You’ll see the amount be debited from your account immediately, and you’ll have a paper draft/cheque made out to the vendor.
You head down to the store with the funds to collect you shoes. If they fit, no problem, you hand over the banker draft, which the salesperson scans, it is validated, and their account is credited with funds.
If the shoes don’t fit however, you head back to the bank, and you can deposit it back into your account, cancelling/invalidating the draft, and restoring the funds to your account.
DBCs in their most raw form, won’t do this out of the box, with a single owner. But, if you give it two owners it becomes like that banker’s draft: either the shoe shop can cash it if you want to proceed with the purchase, or you can deposit it back in your Safe if not.
And there’s the thing, most users won’t be interacting with DBCs in their rawest form (or really need to know what a DBCs is) because we’re building a layer of UX on top of all this. So you can expect various payment solutions powered by DBCs under the hood:
Instant payments: Enter an amount and payee (e.g. @safeshoes) and the payment is transferred across the network immediately. Could of course be a single click operation in an e-commerce scenario too. These can be sent anonymously or not, depending on your needs.
Bankers Draft style payments: As described above, this would be like making out a cheque to a specific payee, but the funds can also be paid back to be should I need it. This could be made out on paper, or sent via other channels on the clearnet, email or whatever. Again, anon or not, it’s up to you.
Cheques with out a payee: This is a method of paying someone a specific amount, when I don’t know their details, or even if they have a Safe on the Network at all. It’s like a cheque without a blank payee. The funds are withdrawn from my Safe, but I can keep track of if they have been deposited, and take them back if I need to. These could be anonymous too, or not, depends on your needs.
Digital Cash: This needs a little more work (@danda is on it!) but the desire here is for ownerless DBCs which would allow users to withdraw cash notes, which anyone could then deposit. If you were given one, you’d want a network connection to validate it, and then secure it through depositing it of course, but it would always be anonymous, for both parties in the transaction.