  We develop a general framework for the study of strong Morita equivalence in
which $C^*$-algebras and hermitian star products on Poisson manifolds are
treated in equal footing. We compare strong and ring-theoretic Morita
equivalences in terms of their Picard groupoids for a certain class of unital
$^*$-algebras encompassing both examples. Within this class, we show that both
notions of Morita equivalence induce the same equivalence relation but
generally define different Picard groups. For star products, this difference is
expressed geometrically in cohomological terms.
