What is the difference between set::key_comp vs set::value_comp in C++? Going to cplusplus.com page there is no significant difference. Furthermore on set::key_comp & related set::value_comp pages last sentence is "(...) key_comp and its sibling member function value_comp are equivalent."
Examples are almost the same:
key_comp defines the order of the keys in a container.
value_comp defines the order of the values in a container.
In a std::set where, essentially, the values are the keys, the two are indeed exactly equivalent. But that's not true in all containers, e.g. std::map, or, in general, in a container that you might build yourself that follows the conventions of the C++ Standard Library Containers.
Note also that http://en.cppreference.com/w/ is a superior reference for C++. It pretty much proxies the standards.