The botargo of Samuel Pepys and the bottarga of Martino de Rossi appear to be extremely similar products to the bottarga we can buy today: that is, bottarga di muggine, or the roe sacs of grey mullets, cured and dried. There are some differences between different cultures' bottarga-like products
The Greeks appear to coat their avgotaraho in beeswax, which acts as a preservative; karasumi produced in Japan and Taiwan is not dried as thoroughly as Italian bottarga, and is a little softer as a result (and is often also covered in wax to prevent further drying). Eoran, the Korean version of cured and dried grey mullet roe, is cured in soy sauce, and is brushed with sesame oil as it dries.