What process fundamentally separates a star like the Sun from planets like Earth or Jupiter?
Answer
Initiating and sustaining hydrogen fusion in its core.
The ability to start and maintain nuclear fusion of hydrogen in the core is the defining physical characteristic that designates a celestial body as a star. Planets lack the necessary mass to achieve this sustained reaction.

Related Questions
What process fundamentally separates a star like the Sun from planets like Earth or Jupiter?What is the specific spectral and luminosity classification assigned to the Sun?By mass, what are the two primary elements composing the Sun?Why is Jupiter classified differently from the Sun, despite sometimes being called a 'failed star'?What crucial astronomical measurement, successfully achieved by Friedrich Bessel in 1838, proved stars were comparable objects to the Sun?Approximately how many times the mass of Earth is the Sun?What causes the Sun to appear as a distinct disc while other stars appear as point sources of light?What is the main reason the Sun retained a proper name like 'the Sun' while other stars were given general classifications?Which type of star constitutes the significant majority of stars found in the Milky Way galaxy?In the Sun's classification (G2V), what does the Roman numeral 'V' signify about its physical state?