I’ll only be answering primarily from the Korean POV.
It’s more complicated than simply being “more” Chinese or Korean, even though there are many more Chinese Jin in the world than Korean Jin. There are two issues at play:
- Not phonetically the same thing. The much more populous Chinese 金 is indeed pronounced Jin/Chin, and the same character is pronounced Kim/Gim in Korean, but it goes far beyond that, as the surnames are both quite diverse within each culture/heritage.
- Different Jin from some different characters. The Korean surname Jin is not from 金. And not even all the Korean Jins are of the same Jin.
I’d like to focus the remainder of my answer on this second point.
In Korea, the Jin family name (진씨) has actually four different clan origins with even more unrelated subdivisions as based on local family lines, many of which don’t have the same phonetic reading in Chinese language(s).
That is to say, if you meet a Korean with a Jin surname, their family surname hanja could be of one of four different characters, and when read a Chinese language context would be the equivalent of a Jin, Chen, Chan, Qin, Tan, or Tang, depending on not just the hanja character used, but also which region/dialect of Chinese is used to render the Chinese character surname. And although the Korean Jin surname as a whole isn’t a super-large group, it’s not an insignificant one either:
- Nearly all Korean Jin family name holders are 陳, of three different clans founded in the south of the peninsula, with a total of about 450,000 registrants (94% of all Jin surname holders). One very unique thing is that it is also among of the largest Joseon-era-founded lineages, although calling it “recent arrival” wouldn’t be quite correct.
- Having just under 20,000 registrants, the much older 秦 line actually entered via the Tang to Bakeje and survived as absorbed into Silla. Note that this line ended up having the clan based in Jeju-do, and its lineage is independent of another 秦 line that was founded during the Goryeo era in Jinju, which appears to have some confusing overlap with other Jin lineages. This line amounts to a little over 11,000 registrants and is the subject of ongoing hereditary research.
- There are only about 7000 registrants of 晋 and just 1500 眞.
Some celebrity Jin surname-holders in Korean entertainment among a few dozen. (clockwise from upper left) actress Jin Ki-Joo, BEATWIN’s Jin Sung-Ho, CSJH the Grace’s Sunday / Jin Bora, Signature’s Belle / Jin Hyunju (whose mother is Filipino), 1TEAM’s BC / Jin Sung-Ho, and 1990s top star/actress Jin Jae-Young