I still don’t get the difference between topic and subject either.

Like apparently I get that the subject is whatever noun is doing the action/the verb. And it took me a while to realise that the “X has a Y” is X은/는 Y이/가 있습니다 because the Y is doing the action of being (이다)  but then it took me an even longer forever to realise that X is the topic apparently. Which is weird because topics were explained to me as “what the speaker is talking about” and that’s such a vague explanation like. When I say I have a cat my English and Hungarian brain would say I’m talking about the cat, or having a cat, but apparently my Korean brain is talking about myself. Which I get that it makes sense but… it didn’t make a lot of sense at first.

And it’s deceiving as well because I always thought the subject comes first cause SOV but apparently not because X in “X has Y” is the topic and Y is the subject. Right? Plus it gets even worse when a location comes. I think a simpler explanation would’ve been “owner + 은/는 (location + 에) owned thing 이/가 + 있습니다/없습니다”.
But then also 은/는 has consistently been translated in the lesson summaries as “regarding me” so I guess if I translate it like that it’s easier to interpret as the topic. “Regarding me, a cat exists” = “I have a cat.” My brain isn’t wired for that yet x)) 

It was the lesson before that when it tried to make me understand the difference but I didn’t cause I’m stoopid.

Like in 제가 여자입니다 제 is the subject.
But how is 저는 여자입니다 where 저 is the topic different in meaning. Like they both mean the same thing, no? Regarding me I’m a woman? Or I am a woman. What’s the diff?