Theses minerals were confused because they are quite similar in appearance, attributes and possible usage.
Graphite was previously called plumbago meaning the mineral Galena also called lead glance, which is a lead containing ore, not pure lead (plumbum). The density of pure lead glance (PbS) is only 7.60 g/cm3. They both look really similar and were indeed used for similar applications, for example namely in cosmetics. Kohl and mascara are charcoal – or mainly carbon – and just this galena respectively. Graphite was previously also quite often confused with molybdenite, (density: 10.28 g/cm3) a substance also capable of marking smooth surfaces.
Going by density alone is not very useful when classifying minerals, since densities vary, despite containing the most wanted metal. The numbers cited by you and me are for the pure compounds, usually not found as such in nature.
Galenit is also quite soft, clocking just 2-3 on the Mohs-scale, compared to 1–2 for graphite.
All of these materials can be used as a solid lubricant as well. Making them of strategic importance for military purposes. England banned the export of pencils to Napoleonic France, since the containing graphite is ideal as a lining for casting cannonballs. (Source: Scientific American: Carbon Wonderland (2088))
Like galena graphite was also used to glaze or line pottery vessels, making them more fire proof.
The three minerals historically named galena, molybdena and plumbago have several common features — they are all soft, dark materials with a metallic lustre. Before the advent of modern chemical methods, these three substances were often mistaken for one another. Because galena (lead(ii) sulfide) was known to be a useful lead ore, it was commonly believed that molybdena and plumbago also contained lead. However, molybdena (which we call molybdenite today) was actually molybdenum(iv) sulfide, and plumbago was what we now call graphite.
(Anders Lennartson: "Made by molybdenum", Nature Chemistry, Vol 6, August 2014, p746.)
Most important is of course the actual application as a writing or drawing tool. Everyone now knows how graphite in pencils works, but a similar effect is achieved in using a stilus plumbeum. These drawing tools are said to originate in ancient Egypt and are allegdly also described by Pliny. This variation of metal point is today most often called a silver point, despite lead being the main component in most cases.
This then closes the circle since modern pencils, containing graphite, are in English often called lead pencil and in German always called Bleistift. Young students often wise crack about licking the tip of a pencil, being unsure whether "it is or is not dangerous" because "lead is toxic", "actually it is not lead and does not contain any lead, so it's safe". At least modern German word usage (and Danish, Dutch, possibly more) and many citizens still confuse the minerals.