Commentaries:
According to the pattern God began in Genesis 48:16, He is establishing that there is a difference between Judah and the other tribes by attaching the name “Israel,” not to Judah, but to those other tribes.
Later, during the time of King David, the distinction continues:
» Ishbosheth, Saul's son, was forty years old when he began to reign over Israel, and he reigned two years. Only the house of Judah followed David. (II Samuel 2:10)
» David was thirty years old when he began to reign, and he reigned forty years. In Hebron he reigned over Judah seven years and six months, and in Jerusalem he reigned thirty-three years over all Israel and Judah. (ll Samuel 5:4-5)
» I gave you your master's house and your master's wives into your keeping, and gave you the house of Israel and Judah. And if that had been too little, I also would have given you much more! (II Samuel 12:8)
These two separate houses had their differences:
Now the king went on to Gilgal, and Chimham went on with him. And all the people of Judah escorted the king, and also half the people of Israel. Just then all the men of Israel came to the king, and said to the king, “Why have our brethren, the men of Judah, stolen you away and brought the king, his household, and all David's men with him across the Jordan?” So all the men of Judah answered the men of Israel, “Because the king is a close relative of ours. Why then are you angry over this matter? Have we ever eaten at the king's expense? Or has he given us any gift?” And the men of Israel answered the men of Judah, and said, “We have ten shares in the king; therefore we also have more right to David than you. Why then do you despise us—were we not the first to advise bringing back our king?” Yet the words of the men of Judah were fiercer than the words of the men of Israel. (II Samuel 19:40-43)
Pat Higgins
The Nation of Israel—Biblical Israel? (Part One)