hep b serology

Can someone explain why my MD would only order a Hep B antigen and Hep B antibody and not a core antibody test?
My md is part of a large hospital and I think the reason is they would only order if the antigen was positive.
But if I have a negative antigen but a positive antibody what does this mean.  I have been vaccinated in the past with 3 shots for hep B.
From my reading it seems that it mean I am not infected, but have immunity.  Probably from the vaccination, but without the core, it seems that I can't make the distinction between being immune due to past immunization vs past infection.
Could someone please help with this?
Thanks

[cajim]

if I have a negative antigen but a positive antibody what does this mean

--You don't have HBV and are immune.