Total anti-HBC vs. IgM anti-HBc

  I recently had a blood test performed - which included Hepatitis B - where the Total anti-HBc was positive and the IgM anti-HBc was negative.  While I have seen many charts showing how to interpret HBV test results, I have yet to find anything showing or otherwise explaining this combination. (Incidentally, the anti-HBs was positive and HBsAG was negative.)
  I was immunized, at one point, for HBV but I never finished the series.  I do not recall when I was immunized, but I think it was 5 or more years ago.  Is it possible that anti-HBs was positive because of the immunization, but that total anti-HBc was positive because I actually had HBV due to an imcomplete vaccination series?  I never had any symptoms.  I believe I am now immune but:
  Am I a carrier?  Could I infect my spouse or children?  Can I donate blood?  Do I need to be concerned with liver damage?  Do I need further testing?
  In summary, how do I interpret test results where the only positive results were for anti-HBs and total anti-HBc?

[HFHSM.D.-D.M.]

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Dear Kaitlyn Tran:
I enjoyed your questions and I believe I will have a lot of good news for you.  Hepatitis B serology