What's the difference between Ledger Balance and Current Balance on a bank's web site?

Most likely it is for charges that have been issued but not cleared. For example Amazon does a few things when you order from them. There is a initial “We call dibs on $200 from this account”. but they don’t technically take the money. But your bank assumes they did so you can’t spend it twice. But it is still technically in your account.

Amazon only really takes your money after the item ships. That is when it should go from Ledger to Current.

Basically what @johnpowell said. The current account reflects final settlements. The ledger can sort of be thought of as your personal “spot” balance. Take for example, in the old days before online banking, you would write a check to a grocery store and it might take a few days to clear and your statement came once a month. You’d make a little note in your checkbook on some lines dedicated to keeping track of your expenses (my checks still have them). Those lines were called a ledger.

Debit cards work somewhat analogously. There are benign reasons why the amount a company stakes claim to would not quite reconcile perfectly to the amount you end up owing. You’ll likely see a small discrepancy between the two numbers if you run a tab at a bar with your credit card; a little bit more might initially be allocated to the card to cover tips. They don’t want your transaction to fail because you decided to leave a tip. Initially, the allocation would be ledger activity. However, you’re unlikely to notice because when you sign your tab, you will have a final settlement. Another example would be if you rent something for the day, a small/temporary claim might be made on your account to give you incentive to return the item.