It was done for us. Fact is, people from different origins look different. We're not better off avoiding saying black, white, brown, red, yellow: we're better off thinking that it's inconsequential to say it. An arbitrary and insignificant point of difference.
As far as I know they're genetically identical (which I'm sure is exactly what the abuser was considering at the time).
To the serious bit - You're talking about potentially two totally different situations though. Do you agree that Paki can be used both as a pejorative and as a term of endearment?
Say there's a fight in a pub between two guys over an alleged grope of a girlfriend. One guy calls the other a "fat ****", the other calls the first a "******* Paki", while an onlooker says "Pakis can't fight". Only the last of those comments is likely to be racist, as it's the only one that discriminates on the basis of it (I say likely because there's still the chance of sarcasm being on the table). If he's fat he's fat, if he's Paki he's Paki (or possibly half Indian). The asterisks are the abusive bits, while "fat" and "Paki" are probably whatever came to mind as an embellishment to the asterisk insult. It could have just as easily been "stretch", "short stack", "mono brow", or "pimple head". Even further, the asterisks aren't exclusively insulting, because people use that kind of irreverence lovingly at times as well.
So, your first example does indeed appear to be racist, your second needs far more hypothetical information to know what's going on with it.