what is the difference between lambda function and std::function in C++11?

Question

In my case, i defined a function in two different ways, fun1 is a lambda function, func2 is a regular std function,but the lambda one doesn't work with variadic arguments template funcction(vat_function).

the code below shows the problem:

#include <functional>
using namespace std;

template <typename... ParamTypes>
void vat_function(std::function<void(ParamTypes...)>,ParamTypes... parames)
{//this is a variadic arguments template function
};

void faa_function(std::function<void(bool,int)>,bool b,int i)
{//this is a std::function as parameter function
};

int main() 
{
    auto func1 = [](bool,int)->void
    {   
    };
    std::function<void(bool,int)> func2 = [](bool,int)->void
    {   
    };

    bool b=false;
    int i=0;
    vat_function<bool,int>(func1,b,i);//only this one doesn't work
    vat_function<bool,int>(func2,b,i);//OK

    faa_function(func1,b,i);//OK
    faa_function(func2,b,i);//OK
}

vat_function(func1,b,i) doesn't work, why faa_function(func1,b,i) works?