European countries don't have a family-centered system like the Koseki (or Chinese Hukou; Wikipedia says South Korea abolished their system a decade ago) where a document represents a family.
But several of them do have a population register (which is individual-centered, but with references up and down in the family tree). In Sweden you don't get birth or marriage certificates. If you want to prove your birth or marriage, you get your population registry extract which shows that you are registered as existing (proves birth) or married.
So they're the same in that they are based on current state rather than collecting event documents. But they're different in that one represents families, whereas the other represents individuals.
Japan also has a separate residency register. While the koseki shows who is in a family (birth/parents, marriage/children), the residency register shows where you live now/before (and is used for taxation). European countries with a population register simply use the same registry for both purposes.
But several of them do have a population register (which is individual-centered, but with references up and down in the family tree). In Sweden you don't get birth or marriage certificates. If you want to prove your birth or marriage, you get your population registry extract which shows that you are registered as existing (proves birth) or married.
So they're the same in that they are based on current state rather than collecting event documents. But they're different in that one represents families, whereas the other represents individuals.
Japan also has a separate residency register. While the koseki shows who is in a family (birth/parents, marriage/children), the residency register shows where you live now/before (and is used for taxation). European countries with a population register simply use the same registry for both purposes.