What is the difference between auto and decltype(auto) when returning from a function?

auto follows the template argument deduction rules and is always an object type; decltype(auto) follows the decltype rules for deducing reference types based on value categories. So if we have

int x;
int && f();

then

expression    auto       decltype(auto)
----------------------------------------
10            int        int
x             int        int
(x)           int        int &
f()           int        int &&