One of these groups is Israel, also known as the Hebrews or just the Jews. The other group is called the Body of Christ. Each group was established by God, and each group has its own set of rules.
Some might object to this and say that God has always worked on the same level with everyone. But God of course has the right to set different rules for different groups of people, if He so chooses. He is not obligated to save any of us, so if He decides to have one set of rules for one group and a different set of rules for another, who's to complain?
To say that God had different rules for Israel and the Body of Christ means that there are two distinct agreements or covenants. Each of these covenants was designed and instituted by God as part of each group's core identity. Israel had the Covenant of Law. The Body of Christ has the Covenant of Grace. These two covenants are not only very different, they are almost polar opposites. Now consider this: If God says one thing to Israel, and then says the exact opposite to the Body of Christ, is there a contradiction? You'd say no, of course not. But if you don't understand the distinction between the two groups, it appears to be a major problem.
Just in passing, with an explanation to follow later on, understand that we Christians today are members of the Body of Christ. We, therefore, are under the Covenant of Grace. ("Duh," some of you are thinking. Okay, moving on..)
Israel's own particular set of rules is pretty obvious. Just look at books like Exodus, Leviticus, Duteronomy, even the Gospels. Lots and lots of rules. It's a little known fact that Jesus made it a point to minister only to Israel. He said in Matthew 15:24, "I am not sent but unto the lost sheep of the house of Israel." He even commanded His twelve apostles to go only to Israel. "Go not into the way of the Gentiles... But go rather to the lost sheep of the house of Israel" (Matt. 10:5-6). Jesus also quoted constantly from the books of the Old Testament and taught adherence to the Law of Moses. God required strict adherence to the rules in order to be saved. We call it the Covenant of Law for a reason!
The Body of Christ's rules are vastly different. Simply put, there are none. All that is required that you be under the Covenant of Grace. To enter into the covenant, one simply has to turn to Jesus Christ in repentance and believe that He died for their sins and that God raised Him from the dead. That's it! Yes, vastly different.
Think of all the books of the Bible. Which ones pertain directly to Israel? Well, there's Hebrews, which (hence the name) is written to Israel. James starts out his book by addressing it "to the twelve tribes which are scattered abroad," a reference to the Twelve Tribes of Israel. Peter's books, John's books, Jude, Revelation.. all addressed to those under the Covenant of Law. So which books are written to the Body of Christ? Well, all the ones that aren't addressed to Israel. The book of Romans, however, takes turns addressing both groups.
To understand the Bible, it is imperative to know which group is being addressed! Once you know, you become better equipped to make sense of otherwise confusing or seemingy contradictory passages.