The defintion of star/planetary/solar system
I think it's largely a matter of personal preference. Some people will want you to be technically correct and only use "solar system" to refer to the Sun and the objects that are under its gravitational influence. Wikipedia defines it as such:


  The Solar System comprises the Sun and the objects that orbit it, whether they orbit it directly or by orbiting other objects that orbit it directly.


NASA says that the term is more general:


  A solar system refers to a star and all the objects that travel in orbit around it. Our solar system consists of the sun - our star - eight planets and their natural satellites (such as our moon); dwarf planets; asteroids and comets.


As an astronomy enthusiast, I do differentiate between "stellar system"/"star system" and "planetary system". I'd use "planetary system" to refer solely to the planets in a system, as well as their moons, while I'd use "stellar system" to refer to the whole thing. That's just my opinion, though, and I'm unsure what professionals use. In casual conversation (especially with a non-expert), you can probably use whatever term you want. If you're using it formally, you should probably do some more research. And while you're at it, check whether or not you should capitalize "Solar" and "System" in "Solar/solar System/system". If people nag you about terminology, they'll nag you about capitalization.