The reason for that distinction is found in older models of planetary formation. The 'inner planets' were those inside the snow line of planetary formation, which determines at what distance from the sun volatile compounds (like water) can condense into dust particles and thereby serve as material for planetary accretion. This means there's a lot more stuff to make planets out of in the accretion disk beyond the snow line, which was long assumed to determine why the planets inside the line are rocky and the ones beyond it are gas giants. It turns out that things are a lot more complicated than that, but that's the origin of the distinction.
Star systems consist of roughly four classes of object: A. objects large enough to ignite internal fusion; B. objects not large enough to ignite fusion but large enough to that their gravity pulls them into hydrostatic equilibrium (a roughly spherical shape); C. objects not large enough to reach hydrostatic equilibrium but with sufficient internal gravity to hold together; and D. tiny dust-like particles.There's another issue that if we stop calling Jupiter, Saturn, Uranus, and Neptune planets (or plane-ettes, or wandering stars, or rudisplorks), we have another question to ask ourselves, "What are they?" I have lots of ideas, but I think the only category that is board appropriate is to call them Space Balls.
Class A is stars and brown dwarfs. Class D is dust grains. Class C is asteroid, comets, and the like. Planets are a sub-set of class B objects, which also includes a very large number of objects that are in hydrostatic equilibrium but are not occupying discrete orbits around the sun because they are either orbiting some other object (ie. moons) or because they are part of a mixed class of objects occupying a zone or belt of numerous objects (ie. Pluto, Eris, and other Kuiper Belt objects). It's worth noting that, at this time, it is not known where the boundary between B and C objects lies, because exactly how big any icy object needs to be to reach hydrostatic equilibrium is a subject of ongoing active research.