From Genesis to Exodus - is God dealing with Israelites or Jews? Finished reading Genesis and now that I'm on Exodus, I get the impression God is dealing with Israelites and not Jews. Is this because Jacob was given the name Israel, so all his descendants were called Israelites?
Yes, that's right.

The origin of "Jew" actually comes from Judah, one of the sons and tribes of Jacob/Israel. When the Kingdom of Israel splits after Solomon, the dominant tribe of the southern kingdom was Judah, and so it came to be called the Kingdom of Judah. Though there have always been descendents of all the sons and tribes of Israel, the prominence of Judah meant that "Jew" came to be used as a synecdoche for the whole of the nation of Israel after the exile.