My understanding:

int a = 1;
   // variable definition =
   // declaration + initialisation

int b; // variable declaration

b = 2  // variable initialisation,
       // type of assignment

a = 3  // variable assignment

int f(int x, int y);
   // function declaration

int g(int z) {
   return z;
}  // function definition

int f(int x, int y) {
   return x + y;
}  // function definition

I would define them as follows:

• Declaration: This thing exists.
• Definition: Here are the details for how this thing works.
• Initialization: Assign the initial state to this thing.
• Assignment: The value of this thing is now X.