Both of these translations are correct depending on whether the verb that follows is negated.
Amíg is actually equivalent to the opposite of until in the same way that unless is the opposite of if. It specifies a case in which the statement of the main clause is not valid or the time period during which the event of the main clause occurred:
- Amíg nem csinálod meg a házi feladatodat, addig nem játszhatsz. - You can't play until you're done with your homework.
- Addig sétáltunk, amíg sötét nem lett. - We were walking until it got dark.
- Zenét hallgattam, amíg a metrón ültem. - I was listening to music while I was on the subway.
Sentences should be translated using the pronoun/wording that matches the intent of the speaker: amíg nem is similar to until and amíg is similar to while.