What does the union and the confederacy have in common together?

There were numerous similarities.

One is that the government system was the same. Although the confederate state placed higher value on state rights than the northerners did, both sides had clearly divided separation of powers and the three branches that constituted checks and balances, as the framers of the original constitution had intended when they were writing it.

They had a very similar social system as well. Although they separated on the question on slavery, the people who weren't slaves lived in a very similar manner. There was a clear class distinction and the numbers of people who belonged to different classes like the upper, middle, and lower, were similar in both sides of the war.

They had a similar military as well. This is where they were the most similar. The weaponry was almost the same and the generals often went to same schools and knew the same things regarding leading an army because they had been working together before the war began. Their behavior was almost the same because of the heavy influence from the West Point school of military which influenced the development of both militaries.