I know you’ve asked this before but I still don’t think I completely understand your question.
Are you asking just about the Lightning Network? An invoice is a single-use text string that contains information about a payment being requested by a node that another wallet can pay.
Once the invoice is paid, either party can check the payment hash to verify that it was delivered. That could be considered a “receipt,” but it’s not really a word used much in bitcoin lingo.
