Are Vampire Stars and Symbiotic Stars the same type of star or is there a difference?
Vampire Stars siphon off hydrogen from its neighbour. According to https://www.cfa.harvard.edu/~kenyon/ss/, Symbiotic Stars seem like the same description.
"In all systems, the hot component - a main sequence star, a white dwarf, or a neutron star - accretes material lost by the red giant." (Harvard)
SS Leporis has been described as Symbiotic Star and in some places as Vampire Stars.