What is important to distinguish
Karta pobytowa is a document, a zezwolenie na pobyt is a permit issued by a decision. First you get a permit, then a card. The same appearance of the cards does not mean the same right to work or the same length of stay.
How to use it
Keep the card with a valid passport when travelling: the card does not replace a passport. When applying for employment, show the employer the decision on the permit as well – the inscription “dostęp do rynku pracy” is not enough to understand all the conditions.
When to act
Check the dates of the card and authorization separately. With an indefinite permit, the expiration of the plastic requires the replacement of the card, rather than obtaining a new permit. With a temporary permit, you can not simply "renew the plastic" instead of a new application.