If I don't understand what my friend is trying to say do I say "That doesn't make any sense", or do I say "I don't understand." Should the two phrases be the same or is there a more polite way of answering towards maybe a grownup instead of a friend? Which phrase is more casual and which phrase is more proper?
"I don't understand" says that "I" can't figure it out - it puts the cause on you.
"That doesn't make any sense" says that your friend can't figure out how to explain it.
So the first wold be more polite.
There may be times when your friend actually doesn't make sense. Then you might say, "Could you please explain that again?".