What is the fundamental difference between value type and reference type?

C# divides types into two categories - value types and reference types. Most of the basic intrinsic types (e.g. int, char) are value types. Structs are also value types.
Reference types include classes, interfaces, arrays and strings. The basic idea is straightforward - an instance of a value type represents the actual data (stored on the stack), whereas an instance of a reference type represents a pointer or reference to the data (stored on the heap).
The most confusing aspect of this for C++ developers is that C# has predetermined which types will be represented as values, and which will be represented as references. A C++ developer expects to take responsibility for this decision.
For example, in C++ we can do this:
int x1 = 3; // x1 is a value on the stack
int *x2 = new int(3) // x2 is a reference to a value on the heap
But in C# there is no control:
int x1 = 3; // x1 is a value on the stack
int x2 = new int(); x2 = 3; // x2 is also a value on the stack!