There seem to be a scholarly debate on the specific difference(s) between multi-methods and mixed methods. To what extent does multi-methods differ from mixed methods?
This question was previously asked on ResearchGate and there were some useful responses: https://www.researchgate.net/post/What_are_the_differences_between_multi_method_and_mixed_method_research_Are_the_both_method_share_the_same_research_design
Multimethod research is a broad term that corresponds to the utilization of more than one type of method (e.g., two or more qualitative or quantitative methods) in a single study. On the other hand, mixed methods research is a more specific term that refers to using both qualitative and quantitative data and methods within an inquiry, emphasizing their integration in the methodological approaches and analytical techniques applied in the investigation. For instance, a study that employed two quantitative data collection methods to answer a question of interest would be characterized as a multimethod study but not a mixed-methods study. You could check out the following publications for insightful input.
Creswell, J. W., & Plano Clark, V. L. (2018). Designing and conducting mixed methods research (3rd ed.). SAGE. https://us.sagepub.com/en-us/nam/designing-and-conducting-mixed-methods-research/book241842
Hesse-Biber, S. N., & Johnson, B. (Eds.). (2015). The Oxford handbook of multimethod and mixed methods research inquiry. Oxford University Press. https://www.oxfordhandbooks.com/view/10.1093/oxfordhb/9780199933624.001.0001/oxfordhb-9780199933624
Some researchers don't have any distinctions between the concept; I have used mixed methods in my longitudinal study using complementary quantitative and qualitative methods, thus allowing for more varied research data (see Helve, 2005, 57-81). The article of Anguera et al. (2018) "Revisiting the difference between mixed methods and multi methods. Is it all in the name? gives some answers to your question.