What is the difference between neurotransmitters acting as neurotransmitters and hormones?
This figure from Campbell (2011), chapter 45, is very didactic and may clarify this nomenclature for you. 

The processes of interest here are a, d and e:



The definition of hormone (in animals) is quite simple: a signaling molecule released in the bloodstream. That's the process a in the figure.

On the other hand, a neurotransmitter is released in the synapse, acting locally. That's the process d in the figure.

However, some nerve cells release their signaling molecule in the bloodstream (process e in the figure). Unlike the synaptic signaling, this molecule can act on a target cell at great distance.

So, despite the fact that we're talking about the very same molecule (norepinephrine in your example), in that last process this molecule is technically speaking a hormone, not a neurotransmitter anymore.



Source: Reece, J., Reece, J. and Campbell, N. (2011). Campbell biology. Boston: Pearson Learning Solutions.