Or whether we use theoretical framework solely for quantitative research and conceptual framework solely use for qualitative research and use both framework for mix-method research?
In academic level, the research proposal and approach can be relative indicators as to the theoretical (existing theory study)framework,
conceputal(specific research)framework/model are used in any particular study.Research can accept a mixed method theory and concept(s) will remain separate but conveniently used for any research study.
Finally, Theoritical framework is implementing the existing and conceptual is application specific and finding some new one's.
In academic level, the research proposal and approach can be relative indicators as to the theoretical (existing theory study)framework,
conceputal(specific research)framework/model are used in any particular study.Research can accept a mixed method theory and concept(s) will remain separate but conveniently used for any research study.
Finally, Theoritical framework is implementing the existing and conceptual is application specific and finding some new one's.
Using a theoretical framework versus a conceptual framework would depend on what exactly you are trying to do in terms of research. If you need a way to organize your data and find a way to develop research questionnaires or interview guides, I would opt for a conceptual framework. If you are trying to prove a pre-existing theory with your results and you have a hypothesis or pre-existing notion of what you will see in your findings, then I would opt for a theoretical framework. Whether to use a theoretical versus conceptual framework is more related to the objective you have in mind rather than the methods.
Here is a paper that might help on the topic: Article Making sense of implementation theories, models and frameworks