In addition to the nice answer by @BrianBorchers (+1), I would like to clarify several aspects that you are interested in (stated in your question), but he hasn't touched upon (if I haven't missed it).
Firstly, I would say that the biggest difference between MBA and master's degree in a business subject is that the former is a general degree, whereas the latter implies some specialization or, at least, focus. Considering this aspect, one could expect that typically an MBA graduate is potentially a more well-rounded business professional than a graduate with a specialized master's degree.
Secondly, I would say that, if you are not absolutely certain about what area of research you want to specialize in, the optimal approach would be to go the MBA route. That would allow you to be exposed to a wider variety of disciplines and areas of study, thus, increasing your chances to find areas of research that best fit your interests, goals and/or personality. An additional positive side effect of this approach is that, should, for some reasons, you decide later to pivot (temporarily or otherwise) and work in a managerial role, you would, in my opinion, have better career options and flexibility being an MBA graduate rather than one with a specialized master's degree.
Thirdly, in regard to MBA specialization, there are indeed many different specialized MBA full programs (or specializations within a general program, also referred to as tracks), in addition to standard general MBA programs. For example, consider this list of MBA specializations at NYU Stern School of Business.
Finally, I agree with Brian Borchers in that you should target enrolling in a Ph.D. program, if you want to become a researcher in business-related areas of study. Such programs are typically offered through universities' business schools (for example, see this program by Stanford GSB).
Some schools also offer a relatively similar degree of Doctor of Business Administration (DBA). Personally, I am not a big fan of this route, since not only the abbreviation can lead to you being confused with a database administrator :-), but, on a more serious note, Ph.D. programs are often more rigorous and, thus, more respectable and valuable than similar DBA programs (though, it depends on institution, as some top universities also offer DBA degrees - in any way, DBA is typically a more applied degree than Ph.D.). In addition to standard DBA programs, there are also specialized DBA programs, like this one, as well as executive DBA programs, like this one.
You might also find useful to read my answer to a related (MBA vs. Master of Science) question.