It's a bit tricky to spot the subtle difference. I can only give some examples. 1. 요즘 내가 바빠. Lately I'm busy. 2. 요즘 나 바빠. If someone asks "Could you do X for me?", you can say the first that implies "요즘 내가 바빠(그래서 못 해주겠다.) - it's polite. But if you say the second, you sound slightly blunt. -은/는 is a TOPIC marker, not a subject marker. -은/는 and -이/가 both can be used in one sentence. For example, 그거는 내가 할게. As for that thing, I'll do it. / I'll do it even if I wouldn't do other things. A : Let's go eat Galbi. B : 나 돈 없어. C₁: 나 돈 있어. C₂: 난 돈 있어. C₂implies "I have money (unlike you / even though you don't have any)" - it sounds slightly arrogant although it's NOT such a big difference. Any phrases with -이/가 sound like an answer or something that explains what the other one just talked about. A : Who is willing to do X? B : 내가 할게. I will do it. C : 나는 할게. C's answer doesn't make sense because nobody said "I won't do it.". A : (looking into the fridge) Where is the piece of cake? It's been here till last night! B : 내가 먹었어. I ate it.

In 내가, -가is a subject class marker which is emphatic whereas -는 in 나는 is a subject class marker without much emphasis on the subject. 내가 행복해 (Among other people,) it is I who is happy. 나는 행복해 I am happy. You always use -가 with 내 and use -는 with 나.