Punjab means five waters. The land between them is divided into five doabs, and the names are how the country was actually described before the province was cut in two.
Sindh Sagar, between the Indus and the Jhelum. Chaj, between the Jhelum and the Chenab, from the first syllables of both. Rechna, between the Ravi and the Chenab. Bari, between the Beas and the Ravi, which holds Lahore and Amritsar. Bist Jalandhar, between the Beas and the Sutlej, which is the Doaba people mean when they say Doaba today.
Three of the five were cut in half in 1947. Bari lost Lahore to one side and kept Amritsar on the other. Only Bist Jalandhar survived whole, on the Indian side, which is why it is the only one still in everyday use as a name.
The map shows all five until 1947 and then stops showing them, for that reason.
Each doab was a revenue division as well as a piece of geography, with its own assessment circles and its own settlement officer, which is why the word survives in the written record long after it left ordinary speech.
The convention is Persian and is credited to the Mughal revenue administration, which needed a way to divide a plain that has no natural boundaries other than its rivers.
Four of the five are wholly or largely in Pakistan. Indian Punjab holds all of the Bist Jalandhar and the eastern part of the Bari Doab, which is why the doab system is barely used here now.