Where does it become harder? The dictionary definition of 'identical' refers to thinks being the same, being exactly equal and alike, etc., so this is one case where I would consider the common sense and the technical definitions to be very similar. I guess you could say that two identical objects are made of different atoms and so are not the same, but as no two separate objects could ever share atoms then it's not a meaningful distinction to bring up. Heraclitus's river and the human body are both examples of the same thing, while we would say that it is the same river or the same river, obviously the component parts (water, cells) are always changing. We accept this because we need to name things, and it's easier to say 'Dave' than 'The Ever-Renewing Dave' or 'The Dave of Ever-Changing Cells'.
Judging by the quick look up that I just did of universals I'd have thought that an engineer would have thought that they do exist and a philosopher would have said yes, so maybe I'm not understanding the idea properly. I do get the cartoon, but I don't think that most people understand the limitations of cloning. Real cloning that scientists can do now, or could realistically do in the future. Hollywood's fault, I reckon.