The pin is the main body of the rivet which will slot through the pieces of material being joined together.
Rivet head
The rivet head acts as a stopper on one side of the fixed materials.
The head will sit on the outside of the material to stop the rivet from sliding out of the material.
Rivet mandrel
The mandrel is slotted into the rivet gun when being fastened. The rivet gun pulls the mandrel part-way through the pin (body) of the rivet, deforming the pin to form a second head, and then snapping off the mandrel.
Rivet mandrel head
The mandrel head expands the body of the rivet then leaves itself buried inside the rivet, creating a second head to secure and fasten the pieces being joined.