The group SU(3) has been used for a microscopic description of rotations in
both the shell model and the interacting boson model but, since the usual
mapping between bosons and the shell model is based on the concept of senio
rity, there is no obvious physical connection between the two SU(3) groups.
Here we establish mappings between the two models which use the SU(3) grou
p, instead of the seniority, as the connection.