What is the difference between Jacob and Israel in the remnant doctrine?
In the remnant doctrine, Jacob denotes the whole nation, while Israel refers to the small remnant within that nation who respond and believe. Though the number of the children of Israel is as the sand of the sea, only a remnant shall be saved, and that believing few are usually referred to as Israel.
Les explains that Scripture reveals a doctrine of the remnant: God has never enjoyed the majority, but has always had a small remnant. He points first to the flood, where only eight out of the billions then on earth remained true to God. Then, when the nation of Israel comes into view, the Word would light on Jacob, meaning the whole nation, but only a few out of Jacob would respond and believe. Those few were usually referred to as Israel. So Jacob pictures the entire nation, while Israel in this context identifies the believing remnant within it. Paul cites Isaiah: though the number of the children of Israel be as the sand of the sea, a remnant shall be saved. God has always had His remnant, even within the nation of Israel.