The subject is what the sentence (or the clause) is talking about, whereas the topic is what the speaker is focusing thir speech on. The topic is usually explained by the main verb of the sentence.
They are not always clearly defined. You use common sense by noting what the speak wants to talk about.
For example, these sentences talk about the subject 저 and 저의 목표.
- 저는 A-대학교에 다니는 유진이라고 합니다.
- 저의 목표는 공무원이 되는 것입니다.
Sub-clauses are often not about the main topic. They just supply the information needed.
- 우리 가족은 10년 전에 제가 태어난 곳을 떠나 도시로 이사했습니다.
(우리 가족 is the topic. 제가 is the subject of the sub-clause 제가 태어난, where I was born, not the main topic.)