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A star system is a gravitationally bound set of a few stars (on a much smaller scale than a galaxy or globular cluster). Examples include Alpha Centauri with three stars, as well as any binary star. Related terms include triple star, multiple star (sometimes used to mean any system of more then one star but sometimes used to mean three or more), and higher order multiple star (specifically, three or more).
The term stellar system also includes single stars, plus objects, gas, and dust gravitationally bound to the star(s), e.g., the solar system.
Use of these terms is not consistent: I find the term star system sometimes used meaning a single star as well, and the term stellar system sometimes meant to imply multiple stars, and often the two phrases are treated as synonyms. The clearer term single star system is sometimes used for single stars such as the Sun and solar system, but unfortunately, there does not appear to be a term that by consensus covers both single stars and multiple star systems, plus their planets, etc.