Julia Sets: Periodic and Non-Periodic Points Explained

[Kortirion]

I'm a little bewildered when reading about these Julia sets. From the definition a Julia set is the closure of all repelling periodic points of a complex map f.
However I read that a Julia set always contain periodic and non-periodic points. Wasn't the definition including only periodic points? What am I missing here.

 

[HallsofIvy]

The "Julia set" in the second definition is the closure of the "Julia set" of the first definition.