What is the difference between Hebrew, Israel, Jew, Canaan, etc.?

Answer:

I'm having trouble with your question because I think there are some problems with definitions.

Hebrew

This was the term to refer to the descendants of Eber. Abraham is the first recorded as being called a Hebrew (Genesis 14:13). All his descendants are also technically Hebrews, though the name typically is reserved for those who are Israelites. Hebrew is also the name of the language spoken by the descendants of Abraham.

Israel

Israel was the name God gave to Jacob when he wrestled with an angel to get a blessing (Genesis 32:28). The name means "Wrestles with God."

Jacob's descendants also called themselves the children of Israel (Exodus 1:7) or just plain Israel (Exodus 4:22). When the children of Israel conquered the land of Canaan, that land was renamed Israel, though this is not common usage. Typically you see "the territory of Israel" or "the land of Israel." After King Solomon, a civil war divided the nation of Israel into two kingdoms. The northern section, containing most of the tribes, continued to be called Israel, though sometimes it was called Ephraim because its capital was in that tribe's territory. The southern section was called Judah because it was mostly composed of that tribe.

Jews

The northern kingdom was eventually destroyed by Assyria, leaving only Judah. It too was conquered, though by the Babylonians, and sometime after their return from captivity, people began calling them Jews, which is a short form of Judah.

Canaan

These are the descendants of Canaan, the son of Ham. It is actually a collection of independent tribes or city-states. The land of Canaan was the territory these city-states occupied. It was renamed Israel after the Canaanites were conquered by Israel. Since God had promised this land to Abraham, it was also known as the promised land.