Rachunek is usually translated as bill and you can use it referring to any paper telling you to pay for something. I'm not sure to what extent bill and check are synonymous and what is the difference between them in English.
bill, "a list that you are given in a restaurant showing how much your meal costs"
paragon or pokwitowanie. paragon in shops, pokwitowanie in other circumstances.
Rachunek can also mean calculation, (or a field of mathematics like rachunek różniczkowy=differential calculus)
I do not know what is the difference between check, bill and invoice, but in Poland documents are officially called "rachunek" if they do not include consumer tax (VAT=Value added tax), because person/company that issues the document does not have to pay it. Otherwise it is called "faktura". Which means my phone or electricity bill, I will say it is "rachunek", but it will be written "faktura" on the document.
In restaurant you will receive "paragon", even though everybody will call it rachunek.
"paragon". Rachunek refers to the paper telling you to pay (e.g. in a restaurant) or to a water, electricity bill . Paragon - specifically to the piece of paper you get after you pay. Is it different in English?
A check is 'a written order to a bank to pay a stated sum from the drawer's account.' The translation of "I did not get a check' would be 'Nie dostałem czeku'. 'Nie dostałem rachunku' would mean 'I did not get a bill/receipt.
Well, "check" makes a lot of sense in a restaurant context (which seems quite probable), but okay, changed to "bill".
This is how I understand this. In Poland there is no such thing as a 'cheque' as we have in the UK. I know this as I have helped a number of Poles who have been paid with cheques for various things but don't know what to do with them. In e-mails they always called them a czek. Rachunek as you say is a bill, usually in a resaurant, and paragon a reciept. So I doubt if cheque is a correct translation of rachunek.
Yeah, it isn't... but it's accepted automatically. Because "check" is a correct translation, especially in the restaurant context, and then Duolingo accepts "cheque" as a British variant of this word, not taking the meaning into consideration :/
True, I don't think I've ever seen anyone write a cheque in Poland...