If an algebra of type $A$ contains a subalgebra which is also an algebra of type $B$, then it is a Smarandache $B$-type $A$-algebra provided the subalgebra of type $B$ contains at least two elements. This generalizes the notion of Smarandache group, where the group of order $\geq 2$ is a subsemigroup of a semigroup. In this paper we investigate a number of such pairings and we deduce a number of conclusions as a consequence.