Can whatever it is get into your shed easily, ie without having to gnaw its way in?
If so, then it could be either.
The droppings look a bit more like squirrel than rat but if there is no easy access to the shed I'd be surprised if it is squirrel and would lean towards rat. We have squirrels in the garden everyday and also have sheds but none have been gnawed into.
However, both are easily capable of doing that sort of damage to plastic storage boxes.
There is easy access into the shed. The droppings are a blue/grey colour which may indicate whatever it is might be eating berries. l have set a trailcam in there now so hopefully the mystery will soon be solved.
Rat droppings are about half inch long ( 12-15 mm or so) Squirrel dropping are slightly more than half that, ( 7-10 mm-ish ) mouse droppings look like a black / brown grain of rice.
Its likely due to the shape that its a squirrel, rat droppings are more uniform in shape. Rather like a large grain of rice.