The difference in law between a bank and any other company that looks after your money for you (for example, a pre-payment for goods) is that a bank is allowed to add your money to its central assets and do what it likes with it, whereas any other company has to keep your money in a separate account until it returns either it or the goods you wanted in exchange. Lots of people think this is the other way round. This means that if a bank goes under, the bank's creditors get to keep your money, and you get to claim back under your country's guarantee scheme, whereas if a different company goes under, your money in its separate account is protected from creditors, and should be returned to you.
A while back I got a random letter written in German that I had to ask a friend to translate for me. Turns out that a few years ago I had pre-paid for some computer equipment that was under development in Germany. The company director had played fast and loose with the rules and used my money to (fail to) develop the product, before the company went bankrupt. Because of this breach of the rules, the company lost its limited status, and the director was personally responsible for the debt to everyone.