The only thing that you can know from Business Analyst II is that it requires a broader or deeper skillset and experience than Business Analyst I.  There is no industry standard on what this means. 

Oftern when companies tag job postings with titles that end in I, II, III, etc., its for there own internal HR.  All you really need to be concerned about is do you meet the skillset/experience required and will the job be fulfilling and challenging.  If the answer is yes, then you are probably a Business Analyst II.  If you have the skills required, but you don't think the job will challenge you as described, then you probably fit better into that organizations Business Analyst III role or higher.

Maybe someday the IIBA will define some kind of standard framework for label and access varioius levels of Business Analysts.  But I doubt it.  They focus more on certifications.  There are (or soon will be) two avaiable now through the IIBA.  The CBAP or Certified Business Analysis Professional which is a very senior  and experience BA.  And the CCBA or the Certification of Competency in Business Analysis which is for a less senior, but still very competent BA.