Is there any difference between explicitly deleting a constructor vs. just not naming it?

In the following code, the compiler complains for ambiguity although one of the constructors is explicitly removed.

Minibox.cpp:26:16: error: call to constructor of 'Minibox<int>' is ambiguous
  Minibox<int> b1 (a);
Minibox.cpp:14:3: note: candidate constructor has been explicitly deleted
  Minibox (T a) = delete;
Minibox.cpp:16:12: note: candidate constructor
  explicit Minibox (T & a) : value(a) {

But it goes fine just removing the line marked PROBLEM.

// g++ -std=c++11 Minibox.cpp
#include <iostream>

// ..................................................
template<typename T>
class Minibox {
public:
  T value;

  Minibox (T a) = delete; // PROBLEM

  explicit Minibox (T & a) : value(a) {
    std::cout << "T & a\n";
  }
};

// ..................................................
int main () {
  int a = 5;

  Minibox<int> b1 (a);
}