For self-injective algebras, Rickard proved that each derived equivalence
induces a stable equivalence of Morita type. For general algebras, it is
unknown when a derived equivalence implies a stable equivalence of Morita type.
In this paper, we first show that each derived equivalence $F$ between the
derived categories of Artin algebras $A$ and $B$ arises naturally a functor
$\bar{F}$ between their stable module categories, which can be used to compare
certain homological dimensions of $A$ with that of $B$; and then we give a
sufficient condition for the functor $\bar{F}$ to be an equivalence. Moreover,
if we work with finite-dimensional algebras over a field, then the sufficient
condition guarantees the existence of a stable equivalence of Morita type. In
this way, we extend the classic result of Rickard. Furthermore, we provide
several inductive methods for constructing those derived equivalences that
induce stable equivalences of Morita type. It turns out that we may produce a
lot of (usually not self-injective) finite-dimensional algebras which are both
derived-equivalent and stably equivalent of Morita type, thus they share many
common invariants.