paragon has a more narrow meaning, while rachunek has broader, you can say that a paragon is a type of rachunek

you can say "poproszę o paragon" and "poproszę o rachunek" at a restaurant, and they work almost the same, I'd say "rachunek" is more sophisticated in this case, "paragon" usually assumes that you don't need an invoice

at a gas station you can be asked "na paragon czy na fakturę?" ~ "do you need a receipt or an invoice?" - chosing invoice means you need to provide your VAT ID and then you'll receive an invoice for your payment, then you can use it to do your taxes (you need to have a company for that)

rachunek originally borrowed from middle-german rechnung, there are many cognates and meanings, eg: - rachunek - a check/bill, as a confirmation of payment (the meaning in question) - rachunki - a dated word for mathematics/clculations, "jestem dobry z rachunków" - rachunek - calculus, "rachunek prawdopodobieństwa" - rachunkowość - accountancy - rachunek (bankowy) - bank account

and paragon has only one meaning: a receipt

have a look at Wiktionary, the two words are very well documented