薬を飲まなければなりませんか。 Do I need to take the medicine? 薬を飲まなくてもいいですか。 Can I not take the medicine? If literally translated, that's what they mean. Essentially, they are both asking about the same thing, "Should this medication be taken?" The first sentence is asking if taking the medication is necessary. The second question is asking if it's okay that you don't take the medication.

Hi Lucero - exactly the same question occurred to me recently. I notice my I-talki language partners using the second form and asked them was it just another was of saying have to do something - they both said yes - and when I asked the difference between the two, they said that the first one was used more in writing, but the second was more common in speech. So I tried using the second form the other day when chatting to my teacher and she didn't correct me, so I figured it must be okay!