These two words raise some interesting philosophical questions about how
me model the world.
It seems to me that specific came from an experiment
tradition in which where were no standards, so things were measured
relative to other common items, as in specific gravity being the density
relative to the density of water, and the specific heat capacity being the
heat capacity relative to an equal mass of water.
On the other hand, density probably came out of theoretical/philosophical
tradition in which one want to distinguish the intrinsic property of an
object which did not depend on its extension from one which did, so mass
and volume depend on extension, but density does not.
Of course both terms got used by analogy in other contexts leading to all
the ideas that have been discussed.