Answer:
Different people use different ways of characterizing case studies, so they end up with a different number.
The United States General Accounting Office differentiates 6 different kinds of case study: illustrative, exploratory, critical instance, program implementation, program effects and cumulative (GAO, pp 37-60).
Yin categorizes three types of case study: exploratory case-study, descriptive case-studies and explanatory case studies (Yin, 1994, pp 4-6).
And Robert Stake also differentiates three: The intrinsic case study, instrumental case study and collective case study (Stake, 1995).
Links/References:
Robert E. Stake, The Art of Case Study Research. Thousand Oaks: Sage, 1995.
Robert K. Yin. Case Study Research: Design and Methods. Fourth Edition. SAGE Publications. California, 2009
GAO