What characteristic fundamentally separates a white dwarf from an active main-sequence star?
Answer
Sustained core nuclear fusion
The consensus reason white dwarfs forfeit the title of 'true star' is the lack of sustained core fusion, marking them as energetic remnants rather than living, fusing objects.

#Videos
Are white dwarfs stars -- a debate! - YouTube
Related Questions
According to the stringent standard used by modern astrophysics, what defines a "true star"?What mechanism supports a white dwarf against gravitational collapse once its thermal pressure ceases?What is the source of the light observed emanating from an isolated white dwarf?What is the critical mass limit for a non-rotating white dwarf before electron degeneracy pressure fails?In contrast to active stars, what counterintuitive physical behavior is exhibited by white dwarfs as their mass increases beyond normal stellar behavior?What characteristic fundamentally separates a white dwarf from an active main-sequence star?What process causes the structural support in the core of a neutron star?What is the expected ultimate fate for about 97% of stars in the Milky Way, including the Sun?Why have no theoretical, non-radiating black dwarfs been observed in the universe yet?What event, involving two white dwarfs, can potentially restart core fusion and create a true star, albeit temporarily?