The former is what you're describing. The latter is where the bank takes the funds from you then itself guarantees the piece of paper. Much more like an arbitrarily denominated bit of cash often used in large transactions in the States when (1) a seller doesn't trust the buyer too much or (2) the seller wants the funds to clear more quickly.
Also, regular checks are great. There's something about having to physically take time to spend money via a goofy little ritual that makes it easier to save the stuff.