A "Culture" needs a "Name"
Culture consists of things like "mother language", cooking of different dishes, the customs etc.
There are 5 major Cultures in Pakistan
1. Punjabi Culture (.... people who belong to this Culture, they are known as PUNJABIES)
2. Sindhi Culture
3. Pushtoon Culture
4. Baloochi Culture
5. Kashmiri Culture
Then there are sub-cultures like:
1. Saraiki culture
2. Barahwi culture
3. Hazara culture
4. Kafiristani culture etc.
All these "Cultures" have separate "Names" through which they are recognized.
The people, who migrated and came from India, they have also a specific Culture, which consists of language, Cooking style, customs etc.
The biggest mistake was to not to give a specific NAME to this separate Culture at time of creation of Pakistan, through which this Culture could have been recognized.
In 1951 Constituion, the name of these People was officially given as "Muhajirs". Since then this name carried on and still exist today.
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2nd: Or to start understanding that Muhajirs has lost it's literal meaning and it has been used now as "Terminology".