What's the difference between the "fractional reserve banking" ratio and the "Basel capital adequacy " ratio?

The answer is, they are a mirror image of each other (but lead to much the same outcome).

* The FRB ratio restricts the ratio of liabilities (deposits) to a specific category of assets (gold coins in the safe) to a certain maximum (let's say ten) and

* Basel ratios restrict the ratio of assets (loans made to customers) to a specific category of liabilities (paid up share capital and retained profits - the bank, as an entity is under no obligation to repay them except as dividends or on a winding up) to a certain maximum (again, let's say ten). Remember also that "share capital and retained profits" are nothing in themselves - the assets are real, the liabilities are real and this is just a balancing figure (in the same way as "equity" in a house is nothing tangible, the house is real, the mortgage is real and your "equity" is just a mathematical or legal concept).

Which is why it is best to avoid the word "reserve" completely, as it can mean two completely opposite things. The FRB banker keeps ten gold coins "in reserve" and the Basel banker has "capital reserves"; the former is an asset and the latter is a liability.

In either case, the banker starts off with "ten" (call it gold coins, millions of pounds, cockle shells, sickles, galleons, whatever) and lends them out. The borrower spends them and the recipient deposits them back in the bank, so they can be lent out again and will be re-deposited and so on until the upper limit is reached.

The idea that banks lend out ten for every one taken as a deposit is a nonsense. Once the dust has settled, under FRB the bank has lent out ninety pence for every one pound taken as a deposit, and under Basel rules, the bank has lent out £1.11 for every one pound taken as a deposit, as the diagram shows (click to enlarge):