Our Sun is a star. It’s a vast ball made up of 74% hydrogen and 24% helium, with trace amounts of other elements. It has so much mass that the temperatures and pressures at its core are hot enough to ignite fusion. At the core of the Sun (and other stars), atoms of hydrogen are being fused into atoms of helium. This process releases a tremendous amount of energy. If an object isn’t performing some kind of fusion at its core, it’s not a star.
Most planets are actually made of similar material to the Sun. Both Jupiter and Saturn have similar mixtures of hydrogen and helium. If the planet Jupiter is made of hydrogen, why doesn’t it shine like a star? It all comes down to mass. Jupiter would need to be about 80 times more massive before it had enough mass to actually ignite hydrogen fusion at its core.
The small rocky terrestrial planets like the Earth and Mars make up just a fraction of the mass of the Solar System. Unlike the larger gas giants, the terrestrial planets are mostly made up of denser elements, like iron, silicon and oxygen. The larger gas giant planets probably have large quantities of these heavier elements in their cores. In fact, Jupiter probably has an Earth-like ball of rock with 14 to 18 times the mass of the Earth at its core.
What about orbits? Planets orbit stars, no question. But you can also have multi-star systems where stars are orbiting stars. And it’s also possible that you could have binary planets orbiting a common center of gravity and together they orbit around a star.
The end of the day, the only real difference between planets and stars is mass – almost everything out there is made up of 75% hydrogen and 24% helium. If an object has about 80 times the mass of Jupiter, it has sufficient mass and temperature to ignite solar fusion in its core. If it doesn’t… it can’t
NASA: Cosmic Chemistry