You may be encountering different uses of the term 'network service', with entirely different meanings.
I have seen the term used to describe 120/208 'single phase' service, such as might be used for individual residences in an apartment building. Such a service is really two legs of a 208/120 wye, and so at the basic physics level is not really 'single phase'; but is used in the same fashion as a residential single phase service.
As to why two legs of a 120/208 service requires a different meter from a 120/240 service: A standard meter for 120/240 single phase service 'cheats' and is not 'blondel compliant'. The 'blondel theorem' basically says that to correctly meter a three wire service you need to make _two_ voltage measurements (say the two leg-neutral voltages), and _two_ current measurements (say the two 'hot' leg currents). A standard 120/240 meter simply makes one voltage measurement (the leg-leg voltage) and then assumes that the leg-neutral voltage is exactly 1/2 of this value. In other words the meter ignores any phase difference or imbalance.
Because of the phase difference present in a two leg 120/208 service, such a meter would read anywhere up to 14% low, not accurate enough for utility metering.
-Jon
