They may have met Pakistani people but aren't going to pay enough attention to know that. They'll just go with some generic Muslim slur (it does not matter if they aren't Muslim).
I am unfortunately around a lot of racists at work (school bus driver). We have a few black drivers so they can't really use the second term you mentioned. They actually use "native" to refer to black people in polite company, a euphemism about as clever as "let's go Brandon".
Its a bit of a linguistic curiosity, because while it’s highly offensive in the UK, here in Boston, it’s a local/colloquial name for “liquor store” (literally, “packie” = “package store” as in “package of booze”). The more noticeable the townie accent, the more likely you’ll hear that term.