I heard from a rabbi that a Jew is anyone who Jehovah gave commandments in the desert via Moses, plus all descendants down the maternal lines, plus anybody that converts. So essentially a series of lineages.
What confuses me is the "secular jew". Because if you don't believe in G-d or the Jewish religion, why would you still believe in the religious definition of what a Jew is?
I suppose it is because they consider themselves part of that community of people.
I was born to a Seventh-Day Adventist mother whose maternal lineage was SDA right back to the founding of SDA. If SDA had that same definition, I'd be a secular SDA. Even more so for me since I was a practicing SDA as a child. But I don't consider myself an SDA at all.