Danish verbs "at ryge" vs "at røge"
Hello, so I've had this question for a while, is there any difference to "at ryge" and "at røge" (this one reminding me of the swedish verb "at röka")"? From what I've seen, both mean "to smoke", and I've encountered both in different situations, like, on the packaging of cigarettes I've seen "Rygning kan dræbe" (smoking can kill), but on some songs (most by Gasolin'), I've seen "at røge" used more often, as in these examples: "(Jeg) Røg på fabrik, og fik mavesår" "Da de første ruder, de røg"
Another thing is, wouldn't they be conjugated as "ryger" and "røger" in the present tense? Is "jeg røg" the correct form in the case of "at røge"?
I'm sorry if this seems like a trivial question, but this is really boggling my mind. Thanks!