Is the English meaning of عذاب really punishment?

Salam alikoum brothers and sisters, When reading Quran I often see the word عذاب translated as punishment. Now, I'm from Moroccan origin and I speak Arabic in a dialect form. What I understand of the word عذاب is suffering and misery. When I look at translation of the word on online dictionaries, I see the same meanings as how I understand it. So why is the word punishment used instead of suffering or misery? If the meaning should be punishment, isn't that the Arabic word عقاب should be used? Jazakoum Allah kheir.