Exactly - a bill is an unconditional demand for payment. Also known as an order. You can find the definitions for "order" in UCC article 3, which is the bible of our currency system's operation.

You have in your hands a bill, and a bill is a negotiable instrument just like the dollars in your pocket - that's right, you have currency in your hand, and you can and should use it to pay that obligation by negotiating it with a special indorsement how I described, without recourse. This settles your legal obligation