In differential geometry a Poisson supermanifold is a differential supermanifold M such that the supercommutative algebra of smooth functions over it (to clarify this: M is not a point set space and so, doesn't "really" exist, and really, this algebra is all we have),
Every symplectic supermanifold is a Poisson supermanifold but not vice versa.
References
Poisson supermanifold Wikipedia(Text) CC BY-SA