~는데: background for what comes next

You already know most of this, because the first part is the modifier from Adjectives before nouns and ~는 것. Verbs take 는, and adjectives take ㄴ or 은. Then add 데.

Take one first clause, 비가 오는데, and put four different second clauses after it. The Korean stays the same each time, and only the English has to change.

Each time, 비가 오는데 says the same thing: it's raining, keep that in mind. "And", "so" and "but" are English's way of spelling out a link that Korean leaves to the listener.

Three kinds of second clause turn up again and again. Don't treat these as three meanings. They're what the same background clause looks like from the other end.

A question or a request. The first clause says why you're asking. This is the most useful one, and it's how you stop sounding abrupt.

The story goes on. The first clause introduces something, and the second says more about it.

Against expectation. Here the second clause clashes with the background, and English reaches for "but".

That last group is why people call ~는데 "but". ~지만 really does say "but". ~는데 only hands you the background, and you notice the clash yourself.

Compare it with what you know. ~아/어서 says A caused B, and its "so" meaning can't lead into a request or a suggestion. ~는데 claims nothing about cause, so it has no trouble there.

You can stop after the background, add 요, and leave the second half to the listener. Nothing is actually said about the point, and that's what makes it polite. A flat no becomes a fact they can draw their own conclusion from.

Example 1 is how you turn down an invitation without saying no. Example 4 is what you say to someone walking off with your bag, and it's far gentler than telling them they've made a mistake. Example 6 is how you answer the phone when they ask for you. 전데요, short for 저인데요, does the same job.

It can also show mild surprise. 이거 맛있는데요! suggests this is better than you expected. As with most of these endings, the tone does a lot of the work, and a sharp ~는데요 can sound like pushing back.

그런데 is ~는데 on 그렇다, to be so. It starts a new sentence and turns everything you've just said into background. In speech it usually shrinks to 근데, which is fine in polite conversation but not in formal writing.

Example 3 is the use the dictionaries translate as "by the way". It follows from the same idea: all that was background, and here's where I want to go now. 하지만 can't do that, because it's only "but".

Now for a different word that sounds exactly the same. 데 on its own is a noun meaning "place". It always follows a modifier, so 사는 데 is a place where someone lives. You usually can't hear the difference, so it's a matter of spelling, and Koreans get it wrong in writing too.

That noun stretches to mean "the doing of something", as in what it takes to do something or what something is good for. So it often comes before 걸리다, 들다, 좋다 and 필요하다.

To test it, try adding 에. The noun can take it, as in 가는 데에, and the ending ~는데 can't. If 에 fits, write the space. Here are the two side by side.