What do we call the collection of planets and their moons, plus smaller bodies, in orbit around the Sun?

The collection of planets, their moons, and smaller bodies that orbit the Sun is referred to as the solar system. This terminology is widely accepted in astronomy to specifically describe our local cosmic neighborhood. The solar system consists of eight major planets, including Earth, as well as their natural satellites (moons), dwarf planets like Pluto, asteroids, comets, and various other objects that are bound by the gravitational influence of the Sun.

In contrast, the term "galactic system" generally refers to the large assembly of stars, gas, dust, and dark matter that make up a galaxy, which is not specific to our solar system. A "stellar cluster" indicates a group of stars that are physically related and share a common origin, while the "universe" encompasses all of space, time, matter, and energy, including all galaxies and systems. Each of these terms is meaningful in its own context, but when specifically discussing the group of celestial bodies interacting with our Sun, "solar system" is the appropriate terminology.