It becomes more natural the more you experience it. While it can be difficult with something like Duolingo because there's no context, when you're having a conversation it's almost always crystal clear who that subject is.
X을 원하다 - I want to get/have something. I want a cat: 고양이를 원해. I want a pizza: 피자를 원한다
X고 싶다 - I want to do something. I want to swim: 수영하고 싶어. I want to see you: 당신을 보고 싶어요