Jewish is an ethnicity, the official religion of the Jewish people is Judaism, im not sure what is the reasoning for it, but the same word is used for both the ethnicity and and people who practice Judaism (i think the logic was "people who convert to judaism are honorary jewish people" but maybe someone with better knowledge can explain it).
I posted this some time ago in another thread but I'll repost it:
Judaism is the religion, Jewish is the ethnicity. The Jewish people are descendants of the tribes of the Kingdom of Judah (the tribes in the related Kingdom of Israel got obliterated by assimilation into the Assyrian Empire after its conquest), who formed part of the larger coalition that made up the Hebrews. The Hebrews were a fairly exclusive Semitic people who worshipped the God YHWH, who they believed to be in a covenant with them and only them, and so they had laws against marrying outsiders to preserve their status as God's chosen people.
After the split into Israel and Judah and the two kingdoms' defeats, many Judaeans (from which the term Jew comes) were taken into exile into Babylon and only freed decades later by the conquering Persians. From there they got conquered by the Greeks and Romans and were forced to disperse after the Romans destroyed the Temple in the first century and crushed the Bar Kokhba revolt in the second century AD. However, they clung to their distinct religious/ethnic heritage rather than assimilate, if possible, with the lands they ended up in, which is why they remain a distinct religio-ethnic group. A lot of modern Jews don't care for the religion but they're still ethnically Jewish.