Definitions
While researchers still argue about the value of the qualitative and quantitative approaches, their definition is rather universal and agreed upon:
- Quantitative - conclusions are derived by means of numerical analysis.
- Qualitative - conclusions are derived by non-numerical analysis means.
There is also the mixed approach, which means utilising both approaches.
Indeed, there is some confusion, with many people attaching these approaches to research questions and to research methods. But only upon the occasion, this practice is correct.
The following article explains this in greater details.
On (Research) Questions
Certain research question call for a quantitative approach. A question such as 'how many people prefer design A', clearly hints that the conclusion must be based on some numerical analysis and numerical data collection.
A question such as 'why people prefer design A' suggests a more qualitative approach. Asking people why they prefer design A is considered qualitative, and the conclusion may be 'most subjects said that design A is better looking'.
Notice however, that many questions can be answered using both quantitative and qualitative approach - it really depends what is the focus of the research. For instance, in answering the latest question 'why people prefer design A', a researcher may employ a survey where subjects are asked to rank (1-5) different design criteria. The results may yield that 80% of the subjects chose aesthetics as the main reason for liking the design. So now we approach the question from a qualitative perspective.
On (Research) Methods
Quantitative, qualitative and mixed are often attached to the term 'research methodology'. As such it is easy to see why many people attach these to specific methods. What's more, it is harder to separate the approach from a method, but well possible!
The obvious example is interviews - most people will see these as a pure qualitative method. But this is incorrect: Given a sample large enough is taken, interviews can be analysed by numerical means (how many interviewees preferred design A). While this is possible, most researchers will claim that if quantitative data is what you are after, interviews are probably least suited for the task.
In surveys, open question are often part of qualitative research, where close questions are part of a quantitative one.
Even observations can be analysed by numerical means (83% of the subjects have smiled when landing on page X).
Given that, the term "qualitative or quantitative research methods" is flawed - the qualitative and quantitative terms are used to denote the data analysis approach, not the question or the methods employed.
However, does picking method X and applying a quantitative data analysis makes it a 'quantitative method'? Most people will live in peace with this definition, same as a 'red apple' means that this specific apple is red (but it can be green as well).
Conclusion
To answer your question directly:
A UX practitioner's accepted definition of what qualitative and quantitative research is that of the rest of the world, given above.
Also, it is important to note that in search for the 'why?', researchers are free to choose between the two approaches. 'Why?' can be equally explained by the quantitative approach as by the qualitative one.
On the question whether these definitions fit with social science research - absolutely yes. I think the real question is whether the quantitative appraoch is appropriate for social sciences. This question has been dealt with brilliantly in this excellent blog. It also mentions the terms 'exploratory' and 'confirmatory' (which I believe is what you call 'exploratory' and 'investigative'). From the blog:
The deductive–inductive dichotomy is one of several used to distinguish quantitative and qualitative approaches to research. Again in practice the distinction may not be so clear; for this reason some methodologists have proposed the terms exploratory and confirmatory: quantitative research can be exploratory and qualitative research confirmatory. Quantitative research is typically associated with theory testing, that is a theory-first research approach, whereas qualitative research is more commonly associated with an inductive or theory-generation approach. However, there is no necessary connection between purpose and approach. Quantitative research can be used for theory generation and qualitative research can be used for theory verification.
