This is because you could chose to define a star system in two ways I guess. As Cody pointed out above many stars have one or several companions. If you define the system as this group of stars then the galaxy consists of approximately 100 Billion star systems.
If you however chose to define each individual star as it's own system (since every star can potentially have their own planets orbiting) then the number would be approximately 400 Billion.
Well by its proper definition a star system (or stellar system) is a small number of stars which orbit each other while planetary system would be the term for non-stellar objects in orbit around a star or star system.
(Go look at a map of the Firefly 'universe' if you want to see how quickly this can get real complicated.
In everyday language people use star system when talking about what's really planetary systems though... Well, OK, in regular everyday language solar system is often used, which is even worse considering that's technically only Sol and what orbits it.