I'm not soooo sure about this, but..

I'm sure a bill is something you have to pay. It usually is a paper stating how much it's going to cost you.

A receipt is a detail of a payment. For example, if you go to a restaurant, after you've paid the bill you'll receive a receipt stating that you've paid for your meal. I think that's no the best example since in most cases the restaurants don't give you a new receipt, you can stay with the bill.

An invoice is a synonymous of bill.

So, the main difference is the obligation about those object. You have to pay a bill, but the receipt is already paid.