Quark family/generation quantum numbers

Shouldn't strangeness and charm be essentially the same quantum number, the eigenvalue of the family operator for family #2 of the quarks, and similarly for top and bottom, for family #3? It appears that the differing names are just a convenience in distinguishing them due to the widely differing masses between the two different weak isospin states in the same family. Family number should be the same (for the particle, and opposite for the anti-particles, of course) for both isospin projection states -- it's the weak isospin z-projection eigenvalue that distinguishes them in a complete eigenvalue set. All the other eigenvalues should be the same. The Particle Data Group doesn't seem to think so though, since their tables distinguish charm from strangeness and bottomness from topness.