The southern kingdom is referred to as Judah and it included the tribe of Benjamin and some of Levi. Through the book of Chronicles it is often referred to as Israel.
The northern kingdom incorporated the other tribes and was referred to as Israel or Ephraim after the largest tribe. Ephraim is a half tribe of Joseph.
|#||King of Judah||King of Israel|
The list above does note correspond chronologically between Judah and Israel.
Judah had 19 kings. They were all sons or relatives of the previous king. Athaliah the queen mother usurped the throne and declared herself queen.
Israel had 20 (or 19) kings. There were several different dynasties. Note that Tibni and Omri ruled different regions of Israel until Omri defeated Tibni.
Israel lasted ~250 years until exile, Judah lasted ~400 years.