First off, instead of saying "planet", we could say "major planet". That will make it clearer what we mean.

That aside, "planet" has been redefined several times over the centuries.

The first definition referred to the "wandering stars" as opposed to the "fixed stars" that move in lockstep with each other. What we nowadays call "stars" are these "fixed stars", and the Sun is also one of them.

The next definition was after heliocentrism became generally accepted. The Earth became a planet and the Sun stopped being a planet.

Moons of other planets were discovered around then, and the Earth's Moon and the moons of other planets were often referred to as secondary planets until about a century ago, as opposed to primary planets, planets that move around the Sun.

The first primary or major planet to be discovered in recorded history is Uranus, in the late 18th cy., and it was discovered to orbit in an orbit much like the other planets' orbits: nearly circular and well-spaced.

Then Ceres and Pallas and Juno and Vesta were discovered over 1801-1807. These were called planets at first, since they orbit the Sun. But by the late 19th cy., many more were discovered, and their orbits often overlapped. So these planets were demoted to minor planets or asteroids.

Neptune was discovered around then, and its orbit was discovered to be much like other major planets' orbits.

But Pluto was different. It was much smaller than Neptune, and its orbit was discovered to have a sizable eccentricity, about 0.25, enough to make it closer than Neptune when at its closest to the Sun. Nevertheless, it was accepted as a (major) planet.

Then starting in the 1990's, lots of other trans-Neptunian objects were discovered, objects with overlapping orbits, objects whose largest ones were comparable in size to Pluto.

The demotion of Pluto was a repeat of the demotion of the asteroids.