What's the difference between a 'recibo' and a 'factura'

There isn't one, much. The dictionary defines them as follows: factura = bill, invoice; recibo = bill, account (eg recibo de la luz = electricity bill). In fact, the word recibo means receipt, so it could be said that you would get one when the bill has been paid. But no, because this all comes from a bureaucratic past (and present) when there was no direct debit. It was simple: you got a factura, you paid it (at the bank, town hall or wherever, in cash) and you got a recibo. Would that it had stayed as simple... In any case, all either seem to do these days is rise and rise.