what's the difference between an invoice and a bill?

An invoice or bill is a commercial document issued by a seller to the buyer, indicating the products, quantities, and agreed prices for products or services the seller has provided the buyer. A bill indicates the sale transaction only. Payment terms are usually included on the invoice. The buyer could have already paid for the products or services listed on the invoice.

From the point of view of a seller, an invoice is a sales invoice. From the point of view of a buyer, an invoice is a purchase invoice. The document indicates the buyer and seller, but the term invoice indicates money is owed or owing. In English, the context of the term invoice is usually used to clarify its meaning, such as "We sent them an invoice" (they owe us money) or "We received an invoice from them" (we owe them money).

A bill is a classification for anything meaning money owed.

So in essence an invoice is a type of a bill.

invoice is a list of items sent to the purchaser

bill is the amount due

There's probably not much difference in meaning. In either case you will have to pay