I stopped to smoke.
The English translation given here is “I stopped to (have a) smoke”.
This is different from “I stopped smoking”.
Przestałem palić seems more like the second to me, especially as palić is imperfect.
I think the Polish for “I stopped to smoke” is closer to “Przestałem żeby zapalić” no?
Yes, you’re right about this one. Feel free to report this if you run into this sentence again.
“I stopped to smoke” would be “Zatrzymałem się, żeby zapalić” if we assume that the person stopped walking.
Theoretically it could also be “Przestałem, żeby zapalić” if the person stopped some other action – but the action would need to be clear from the context, or else the sentence sounds rather awkward.