a Network Engineer is entirely different from a Systems Engineer. Systems Engineers are simply IT professionals that provide maintenance of computer and networking equipment. they install equipment, do upgrades, maintain, config etc.
A Network Engineer is mainly involved in network design roles like network architecture design, network performance test, some network maintenance etc. Most Network Engineers hold a CCIE or at least a CCNP, MCSE certifications etc. Software Engineer is usually the person that is a problem solver, plans, get software requirements and analysis using UML and systems engineering approach, following the SDLC, designs the software systems and passes the design down to the programmers also know as developers and the developers implement and write the code, test, debug etc. the whole software team follows the Software Development Life Cycle.