Rabbi Mordechai Becher at Aish.com says that we are a nation united by our common heritage. So two Jews could see themselves as members of a nation.
A more limited definition of the relationship between two Jews would be to say that they practise the same religion.
Are there halachos that follow only from being members of a nation and would not be in force just because we have the same religion?
For example, does the concept of כל ישראל ערבים זה בזה – every Jew bears the responsibility of the mitzvah observance of every other Jew - flow from nationhood or common religion?
EDIT Following the useful responses, another way of expressing the question is "are there any halachos that are better categorised as national in origin rather than Bein Adam le-Chavero?"