The difference between the two is a distinction we dont have in Engljsh. (은)/는 is a topic marking particle. (이)/가 is a subject particle, so ~이/가 are used to simply identify the subject of the sentence. They do similar things because the topic of the sentence is similar to the subject, however topic marking particles (은/는) imply a contrast whereas the subject particle (이/가) does not. 은/는 imply something is different than others.
_subject marking 그 가방이 바싸이에요 (That bag is expensive)
_topic marking 그 가반은 싸이에요. (That bag, unlike the other, is cheap)
I sort of think of the topic marking particle as adding stress/emphasis. So if i said "this bad is cheap" without any stress then it just means the bag is cheap, but if I stress 'that' it can somewhat imply that other bags arent cheap. THAT bag is cheap. Or adding the words "as for". As for that bag, it's cheap.
Specifically, looking back at 저는 and 제가, think of 저는 as saying "as for me, I am..." and 제가 as just "I am".
Here is a great podcast and pdf that explain it!
Another thing to know is you dont always need the subject and topic particles. Some people wont use them so it's important to know the word without the particle. But better to use the paticle and not need it than have a confused listener!
Hope this helps!
Thank you SO MUCH for this amazing and clear explanation! I've been struggling with those until I read your comment :D
비싸예요 is grammatically incorrect, and this doesnt entirely portray the contrast of the two particles right. i did a written explanation here:
but the truth is, you wont need to worry about it until you start to make lots of long, multiple clause sentences.
I believe it's 비싸요, because it is a verb (descriptive), not a noun.
이에요 / 예요 would connect with noun as it derives from 이다. The formal polite form is 입니다