The accusative case indicates the direct object of a verb:
Kupiłem ten rower. (same ending as nominative)
Skręcz mi jednego
Już kupiłeś tę
confusing, so I'll let someone else explain and maybe I might learn something
sometimes it's the same as the nominative, sometimes the same as the genitive, but with grey areas in between.
functions de facto as nominative
There are differences.
You will hear kids call to their Mum the vocative "Mamo" rather than "Mama" which would be the nominative. This a > o change is quite common. I'm not sure if it works for all feminine nouns (and masculine nouns with the nominative ending in -a, eg. poeta > poeto).
If you call someone a dick, you call them the vocative ch**u rather than just ch**.
Ksiądz is priest. To address a priest vocatively, the word is księże. Once again, masculine nouns are more confusing. For names, it seems common enough to use the nominative.