No only Urdu Speakers are Mohajir, they have copyright.
My Urdu speaking uncles etc do not call themselves mohajir, I don't know why still so many MQM walay want to call themselves Mohajir.
The poorer ones are short in height, try meeting Urdu Speaking elites who migrated from Delhi, UP etc. They are usually tall, more taller then Pushtuns and Punjabis from urban areas. Many Punjabis get the shock of their life when they actually meet a UP wala, they seem to think that Urdu Speaker=dark, short Hindu background and weak. Army and Police learned it the hard way during 92 operations.