Is every lambda function an anonymous class?

auto a = [](){};
auto b = [](){};
vector<decltype(a)> v;
v.push_back(a); //ok
v.push_back(b); //compiler error

a and b have different type.

I am wondering if each lambda function actually is kind of anonymous class, whenever we create a lambda function, we create a new class with a random name which only visible to compiler ?