The primary difference between the two is when you connect more than one series slat, the slats will fire in a series, and when connecting more than one parallel slat, the slats will fire in parallel. If you only have one slat connected to your module, there is no series or parallel circuit unless you are also connecting to your module directly in which case the single slat will always fire in parallel to the onboard cues. When using series slats, you should always have the shunt (small plug) at the end of the final series slat.
Series and parallel wiring each have pros and cons; see Continuity Clarified for more information on this topic.