Short answers, pulled from the story.
Greek astronomers called Venus, Jupiter, Mercury, Mars, and Saturn planets. They also counted the Sun and Moon as planets to make a total of seven wandering lights distinct from fixed stars.
Pluto was discovered in 1930 after irregularities in Neptune's orbit prompted a search. It was reclassified as a dwarf planet on the 24th of August 2006 when the International Astronomical Union voted to separate it from the eight official planets.
There are 20 moons in the Solar System massive enough to achieve hydrostatic equilibrium known as planetary-mass moons. Both Ganymede and Titan are larger than Mercury while Titan has an atmosphere thicker than Earth's.
Mike Brown notes that abandoning the clearing criterion could raise the number of planets from eight to more than 50 with hundreds potentially discovered later. He argues that location should not matter if an object is large enough to have features like methane lakes.
The International Astronomical Union released a working definition in 2003 which was amended in August 2018 stating an object in orbit around a fusing star is a planet even if identical to a sub-brown dwarf elsewhere.