Pathan, Pashtoon and Pakhtoon are exactly the same thing. Different names for the same ethnic group. The word 'Pathan' is more often used in Urdu while the people call themselves 'Pashtoon' or 'Pakhtoon.' That's why the province was named Pakhtunkhwa. Pashto is the language of the Pakhtuns.
Dari is an alternative name for Persian (Farsi) that is used in Afghanistan. Persian is the official language in three countries:
1. Iran, where it is called Farsi.
2. Afghanistan, where it is called Dari.
3. Tajikistan, where it is called Tajiki and uses the Russian alphabet.
In Afghanistan Dari is the official language, like Urdu is in Pakistan. All/most Pashtuns in Afghanistan also speak Dari, like Pashtuns in Pakistan speak Urdu. Pakhtuns are a majority in Afghanistan, although there are more of them in Pakistan. The Taliban are mostly Pakhtuns which is why Pakistan supported them.
Urdu itself is a hybrid mixture of Indic/Persian/Arabic. In everyday conversation it inclines towards Indic, but in formal speech it becomes heavily Persian/Arabic. Persian speakers find it easier to learn Urdu than Pashto and Urdu speakers find it easier to learn Persian than Pashto.
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