Perhaps one could talk about the units of PPP by talking about converting Greek GDP from "Greek Euros" to "German Euros." But that doesn't mean that the "Greek Euro" is a different currency.

It is useful to know that the cost of living in Greece is lower than the cost of living in Germany. That is, it is useful to know the PPP conversion factor. It is useful to think about GDP per capita in both nominal and PPP terms, to understand what life is like for the average individual. But what use is total GDP in PPP terms? Merely knowing that it differs from nominal GDP is a roundabout way of finding the PPP conversion factor. That's like saying that BMI is useful because, with height, it allows me to compute weight.