This is not definitive by any means, but in a gist, a Network character is any character that resides within the Network and is based off of some kind of real-life digital entity. Honestly, there are no restrictions regarding a character's design, other than (generally) the size cannot be bigger than an OS if the character is not an OS (there are exceptions depending on power, though).
I use Network and system synonymously, but a Network is the whole of all/some connected systems. A system is an individual "Network."