what's the difference between the default and default constructor

This creates a new instance of the type A by calling the default, parameterless constructor:

A a = new A();

This assigns the default value for type A to the variable a and does not call any constructor at all:

A a = default(A);

The main difference is that the default value of a type is null for reference types and a zero-bit value for all value types (so default(int) would be 0, default(bool) would be false, etc.).