V + -는 거야 used for explaining the action about which the listener has some information. V + -고 있어/다 used for explaining the action about which the listener has no information. For example, Q: 지금 뭐 하는 거야? : What is that you are doing now? (The speaker saw some actions or heard some noises.) A: 책 읽는 거야. : What I'm doing now is reading a book. Q: 지금 뭐 하고 있어? : What are doing now? (The speaker has no information) A: 책 읽고 있어. : I'm reading a book.

Actually, -는 거야 and -고 있다 are two almost unrelated constructs. -는 거야 is a way of presenting an idea (description tool) while -고 있다 is a tense expression. 1. -는 거야 is a colloquial form of -는 것이다, literally "it is that ...". It is a widely used ending form to capture an idea in a nested sub-clause to make it indirect and objectified. Instead of treating the idea as the main thing in the foreground, -ㄴ 것이다 describes it as if it's something one is observing from the outside. For example, 1 나 지금 숙제해 = I am doing my homework. 2 나 지금 숙제하는 거야 = It is my homework that I'm doing (or something like that - there's no definite translation) 3 나 지금 숙제하고 있어 = It is my homework that I'm doing. (The #2 -거야 version sounds like it's said from an observer's viewpoint, more detached compared with #1. This might appear somewhat similar to the -고 있다 of #3, but it is actually different) - 그는 그때 이미 죽었다 = He was already dead at that time. - 그는 그때 이미 죽었던 것이다 = It turns out [The truth is] that he was already dead at that time. (The -ㄴ 것이다 version makes it like looking back on the past compared with the short version.) 2. -고 있다 is the present progressive tense form, like "be VERB + -ing" in English. - 동생은 책을 읽고 있다 = My brother is reading a book. - 밖에는 비가 내리고 있다 = It is raining outside.