  We introduce various versions of spin structures on free loop spaces of
smooth manifolds, based on a classical notion due to Killingback, and
additionally coupled to two relations between loops: thin homotopies and loop
fusion. The central result of this article is an equivalence between these
enhanced versions of spin structures on the loop space and string structures on
the manifold itself. The equivalence exists in two settings: in a purely
topological one and a in geometrical one that includes spin connections and
string connections. Our results provide a consistent, functorial, one-to-one
dictionary between string geometry and spin geometry on loop spaces.
