Commonly translated as the "people" of Israel, not the "nation" of Israel.
The Jews are a people. They are not a closed system but have rigorous entrance requirements.
am (ayin mem) is translated as either nation or generic people depending on the context and in this context both apply. Am haaretz the context is generic peoplehood, am cohanim refers to nationality .also virtually all nations have ways to incorporate an alien be it citiazenship test or Halachic coversion mit a beis din.