The Sun's core is slowly converted to Helium from Hydrogen Fusion reactions. While the center collapses and heats up, the outer atmosphere responds to this increased central temperature by expanding away from the hot core. So begins the Red Giant Stage.
The Sun will expand to the distance of Venus, and literally scorch everything on the surface of the Earth until it is nothing but a lifeless rock (no oceans or atmosphere).
As the atmosphere expands, it also becomes VERY thin. At some point, we will be able to peer directly THROUGH this outer atmosphere, and see the very hot collapsed core of the Sun! This is the Planetary Nebula Stage.
Planetary Nebulae have NOTHING to do with Planets. A Planetary Nebula is a shell of hot ionized gas (seen in atomic emission lines) expanding away from the very small, very hot, central star. Click HERE for an animation of a dying star.
This central hot star is the former red giant core. It is called a WHITE DWARF.