We define a structure type to be a faithful functor
from some groupoid to core(FinSet), which is the groupoid of finite sets and bijections. Equivalently, we can think of it as a presheaf of sets on the groupoid of finite sets and bijections, or in other words a functor
These two points of view are related by the Grothendieck construction:
But since a groupoid is equivalent to its opposite, we can also think of a structure type as a functor
In this guise, a structure type is more commonly called a (combinatorial) species of structure, or species for short.
A structure type is a special case of a stuff type, so see stuff type for more information.