The examples you gave come in two classes:
Watchmakers that became Jewelllers: Piaget, Chopard, Patek Philippe (sic), Omega (double sic).
Jewellers that became Watchmakers: Bulgari, Cartier, Harry Winston, Van Cleef Arpels, Tiffany (sic).
But seriously, I only comment on the red ones, like you did.
They do have an additional style element....most likely due to having both watch and jewellery design teams.
Regards,
MTF