@ChiisanaKori 제 is like 내 but in formal speech. 내 is just shortened form of 나의 and for 제 it’s the shortened form of 저의. 제가 vs 저는 depends on the context of the sentence whether the “i” or in this case the “저” is the subject or object
Actually it is not just between formal tone and informal tone. 저 shows the courtesy when you talk to a person whom you are not close to or who are older than you or in a higher rank than you. 나 implies you don't need to show that courtesy maybe because you are close to the addressee or you're older or in a higher rank than the addressee.
Starting with 제, 저 and ending with 니다, 니까, 요(Or other endings from those respective levels of speech) = 존댓말 or formal = To olders/elders Starting with 내, 나 and ending without the ones listed above = 반말 or informal = Between friends 저 can not be used with 아/어/여 (or other endings from that level of speech). 저, by its very nature, is humble and shows more respect than 나. Therefore, it cannot be used with 반말 ("informal"). 나 can not be used with ㅂ니다/습니다 (or other endings from that level of speech). 나, by its very nature, is casual and not as respectful as 저. Therefore, it cannot be used with 존댓말("formal").
e.g : I am from America : 존댓말 : 저는 미국에서 왔어요 & 반말 : 나는 미국에서 왔어
I am studying Korean : 존댓말 : 저는 한국어를 공부하고 있어요 & 반말 : 나는 한국어를 공부하고 있어
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