I can’t find an answer that explicitly says that a case study is a type of research (e.g. analytical research paper, persuasive research paper, definition research paper, etc.). There’s this site that says that a case study is a research methodology (it’s the third chapter of a research paper).
The case study is a qualitative research method in several disciplines, mostly in the social sciences.1 A research paper that builds on this method might also be referred to as a "case study".2
1 See e.g. Gerring, J. (2007) Case Study Research: Principles and Practices (Cambridge: Cambridge University Press).
2 See e.g. Hooghe, L. (2005) ‘Several Roads Lead to International Norms, but Few Via International Socialization: A Case Study of the European Commission’. International Organization, Vol. 59, No. 4, pp. 861–898.
A "case study" can mean several things:
A small[*] piece of original research that was published as part of another research paper or review. For example: a paper describes a theory and subsequently applies it to a small and well-defined subset (a case) of possible applications of the theory, thereby providing anecdotal evidence that the theory is useful,
Particularly in the social sciences, a "case study" may be described in a separate paper, and present anecdotal evidence (or contradiction) of a theory that was published elsewhere. (So similar to (1), but the "case study" is now a separate publication)
A study that is not published in a peer-reviewed journal, but used for example to promote new equipment from a commercial manufacturer by demonstrating its usefulness for the given "case" (this is also called "application note").
Note also that some journals have very specific requirements for the publication types they accept, and that those types are defined by the journal in question.
[*] see commments