Traditional standards on Judaism are clear about the topic. One is only legally Jewish if they have a matrilineal connection to the community.

That being said, I've heard a few people throw around the term Zera Yisrael when discussing the topic. While a Jew is B'nai Yisrael, a Zera would be considered a seed of the nation while not being a legal member of the Jewish nation.

I was curious if such a term is just a modern concept we've developed or if there is historical and Rabbinical precedence in differentiating a person from Jewish origins from the rest of the population.

While they don't have legal Jewish status, are they somewhat held to a different standard when discussing the rest of the non-Jewish world?