I would like to Understand [Spirituality & Religion]

I met a young man who introduced himself and stated that he was Jewish but he meant it as far as an ethnicity. I know a woman who has called herself Jewish but was referring to the religion and not an ethnicity. Now I've heard both in different settings and I've heard people debate about whether being Jewish can be both. I am genuinely curious does Judaism only pertain to religion or can being Jewish include ones genetic makeup or is it very individualized and personal? I don't want to be ignorant or insensitive to the culture.