It depends on which way you will classify it.
If you classify it by purpose then you will have an exploratory, descriptive and explanatory research. Exploratory research is made when there's a little knowledge about it then an author written something new about the topic; while descriptive research, as the name implies, are for to describe the characteristics of a certain sample or population; and lastly, an explanatory research answers the question "why" of a descriptive research.
It can also be classified in terms of its use in which you will have a basic and applied research wherein basic research advances fundamental knowledge about the human world and applied research is a more specific one that tries to solve a certain problem.
Data collection method used could be another way to classify research as there are quantitative, has specific numerical data, and qualitative research - does not have specific numerical data.