Hebrew, Israelite, Jew, Israeli: What’s the Difference?

Every week, I answer a common question related to the end times. Today's is about the difference between a Hebrew, an Israelite, a Jew, and an Israeli, and how Gentile believers fit into God's plan.

Question:

My husband and I are confused about all the different terms used for God’s chosen people. What is the difference between a Hebrew, an Israelite, a Jew, and an Israeli? Is being Jewish a matter of ethnicity, personal choice, or religion? And how do Gentile believers fit into all of this?