A superkey is defined to be the set of attributes in a relation which can uniquely identify every tuple in the relation.
A candidate key( primary key or alternate keys) is a minimal super key.
If a set of attributes can uniquely identify every tuple in a relation, then it becomes a super key. But if there exists a subset of attributes in super key then that forms the candidate key.
if there exists no subset in superkey, then that superkey itself becomes minimal superkey and hence a candidate key.
in your table, S.name and S.age becomes super key but it includes a candidate key S.age. Here S.age can also uniquely identify every tuple.
S.age is candidate key and (S.name , S.age) is super key.
On the other hand, if neither S.name nor S.age can uniquely identify every tuple, then (S.name,S.age) is candidate key as well as super key.
Super key always includes candidate keys, may be primary key or alternate keys.