Thanosaekk has a good timeline but I think it’s important that you talk about the “warlords.”
Yuan Shikai led what was called the Beiyang Army. It was this army that had the lion’s share of the Qing’s modernization and the they’d even been getting help from Japan to build three divisions to send to Europe to fight in WW1 (This was actually just Japan buying influence.)
Anyway, the Beiyang army generals split up after the death of Yuan Shikai and the collapse in central authority… but the Anhui Clique, the Zhili Clique, Fengtian clique… all of them saw themselves as being part of the Republic of China and the one legal continuation of it. They were not separate countries and they didn’t see themselves that way. They were essentially all leading a coup against the others. The “Clique” in their names title refers to how each one was a grouping of generals.
A good book on this is “Warlord Politics in China” by Hsi Hseng’chi https://www.amazon.com/Warlord-Politics-China-1916-1928-Hsi-sheng/dp/0804708940
In the South, the KMT was different. All of the cliques in the North saw themselves as still part of the Yuan Shikai’s Beiyang government and derived their legitimacy from their previous positions in that government. Sun Yat Sen’s government in the South was different and had a different constitution and regarded the government of Yuan Shikai and the successor cliques as all illegitimate.
I see that there are 3-4 Between Two Wars episodes on China. Traditionally, historians split this era into two periods. The Warlord Period (which runs from the death of Yuan Shikai in 1916 to the end of Northern Expedition in 1926) and then there is what’s called the Nanjing Decade which runs from 1927 to 1937.
They are different. In the Warlord Period, the communists are allied with the KMT. In the Nanjing Decade, they are recipient of 5 Extermination campaigns. In the Warlord Period, Japan is mostly content to talk to people. In the Nanjing Decade, they start their salami slicing of China. In the Warlord Period, Sun Yat Sen is in control of the KMT. In the Nanjing decade, Chiang Kai Shek is in control.