Hot, but Not a Star
Although we speak loosely of the central star of the planetary nebula, the very high temperatures exhibited in
the diagrams of the left panel come not from fusion but from retained heat and gravitational contraction.
So strictly, these are no longer stars.
However, if no confusion is likely
we will often refer to white dwarfs (and protostars) as "stars",
even though they are not producing their energy by fusion.