What is the difference between в тишине and в тишину? I know the first one is the prepositional singular of тишина, and the second is the accusative singular of тишина, but I don't really understand the different use cases.
This question arose from the lyrics from a song, specifically: Она на полупальцах в тишину. Here I would have thought it should be в тишине? Or is it because she is moving towards silence, as opposed to in it?
Your guess is correct. "В тишине" is being in a silence, while "в тишину" is a poetic expression (and you will hardly encounter it in a colloquial conversation, as well as «на полупальцах» by the way)- she went away into the silence. For instance, "он сидел в темноте и думал" - he was sitting in a dark place, while "он ушёл в темноту" - he went away into the darkness.
Regardless of whether the expression is used in a poetic sense or not, asking the above questions will help you define the correct spelling or reading of the written words
