는데 used for describing beforehand about a situation which is related with the next clause in order to explain, ask, suggest something. It can be used for attracting attention or giving suspense. e.g. 내가 텔레비전을 보고 있는데 전화벨이 울렸다. 그 애는 노래는 잘 부르는데 춤은 잘 못 춰. 눈이 오는데 차를 몰고 나가도 될까?

~는데 is a sentence connector, but it's a bit... softer than a sentence with the word 'but'. It roughly translates to 'though', or 'but' in English. For example, take these sentences. I want to eat, but I have no money so I can't. Though I have no money, I want to eat. I have to go, but I don't have my car so I can't. Though I don't have my car, I have to go. I need the electricity, but there's a blackout so there isn't any. Though there is a blackout, I need electricity. In the 2nd sentence of all the examples, the word 'though' makes the sentence more softer than using the word 'but'. That is kind of an example of when ~는데 is used. ~는데/은데 will mean 'but' or 'though' in the middle of the sentence. For example, this Korean sentence: 먹고 싶은데, 돈이 안 가져오서 못 먹어요. Could translate as: I want to eat, but I didn't bring any money so I can't. I want to eat though I didn't bring any money (so I can't). I want to eat and I didn't bring any money so I can't. Or this sentence: 저는 밖에 놀고 싶은데 비내려요. I want to play outside but it rains. Though it rains, I want to play outside. I want to play outside and it rains.