The guy in New York was bearded, Muslim, had a foreign name, and from Uzbekistan originally. He may have had white skin, but no one is going to associate him with the typical white guy in the US/UK.
If the shooter was Australian, white skin, had a normal name, and wasn't Muslim, he'd be considered "white" and politicians would be hesitant on using the terrorist label.
If the shooter was Mexican, politicians in the US would most likely have an aggressive response and immediately talk about stronger borders, walls, and vetting.
It's the distinction between being "one of us" vs "one of them", ultimately.