One of the main differences is a Vector analyzer will give impedance change versus time. Say you have a mechanical component which has an inductance associated with it and the inductance is a function of mechanical position. And then you want to know the impedance of the inductance as it is moving. Or say you have a SAW filter and you want to know how its impedance changes with a frequency dynamic signal.
a scalar network analyser will give the magnitude information but not the phase information
whereas a vector network analyser will give the phase info as well
for instance the sna will give the vswr of a circuit whereas the vna will give (on a smith chart ) the magnitude and angle of the circuit