Firstly, the answer is simple with a geographical reasons! Pakistan’s Punjab is a huge Punjab of a very small Pakistan. Our Punjab is a small Punjab of a very huge India.
But if we look into the history of how Punjab formed and all, it have some political reasons too!
How Punjab was formed?
The region was firstly under the mughal rule and sikhs with a very low population resided in the forests and were divided into 13 misles. Despite frequent attacks by mughals, sikhs were able to defend themselves due their skills and fighting techniques .At one time sikhs defeated Mughals and they set up a Sikh Empire under Maharaja Ranjit Singh with Lahore as its capital. the Empire extended from the Khyber pass in the west to western Tibet in the east, and from Mithankot in the south to Kashmir in the north. This later became to be known as Punjab (land of five rivers).At that time also it was a very rich, peaceful and secular state. Punjab was last state to be annexed by Britishers due to its highly skilled army after the death of Ranjit Singh.
After Britishers annexed Punjab, kashmir was seperated
In 1947, when we got independence, a seperate muslim nation was formed. Punjab was divided into two parts as muslims were in majority.
Within British India, the border between India and Pakistan (the Radcliffe line) was determined by a British Government-commissioned report prepared under the chairmanship of a London barrister,, Sir CyrilRadcliffe.
Till the end there was no idea about the two cities (Amritsar and Lahore) while every part of line was finalized . Then at the end , it was decided that Amritsar would be part of India and Lahore (capital of Punjab) as a part of Pakistan.
And Indian Punjab was divided into 3 parts on the basis of language
Pakistani Punjab is yet to be divided into Punjabistan,Hindkostan and Saraikistan. The saraiki and hindko speaking people in pak Punjab are demanding a separate province.