According to May, an operad $\mathcal{C}$ valued in sets is equivalent to a monad in Cat on the endofunctor $C\colon X\mapsto \coprod_i \mathcal{C}(i)\times X^i.$

According to Leinster, an operad is equivalent to a monad in the bicategory of modified spans, diagrams of the form $T1\leftarrow C\to 1,$ where $T$ is the free monoid functor.

Is there some connection between these two monads, other than the fact that they unravel in base cases to the definition of an operad?