Here
std::priority_queue<int, std::vector<int>, std::greater<int> > my_min_heap; std::greater<int> is a template parameter, note that it is inside <>. It is a type. On the other hand, here
sort(a.begin(), a.end(), greater<int>()); an instance of that type is created and passed to sort. Also sort has a template parameter for the comparator, but it is deduced from the argument (to be of type std::greater<int>), so there is no need to specify it explicitly.
More specifically std::greater<int> is a functor ie a type that has an overload for the function call operator. To create an instance and use that to compare two ints you could write:
bool x = std::greater<int>()(5,3); /* the type */ // ^ call constructor // ^ call the objects operator() However, typically the same function object is reused for many comparisons, as is the case with std::sort.