Any Japanese visa would fall under either a "activity visa" (e.g., working, studying, etc.) or a "status visa." Amongst the status visas, long term residents and permanent residents have no labor restrictions. The rest of the visas have restrictions on what activities you do and which institutions are supporting you while you are in Japan. Below you will see visas in each category as well as links for further details.
Just remember, meeting all criteria of a visa does not mean you are guaranteed to have a visa. Because each individual circumstance is unique, we suggest you contact us for your individual specific inquiry. Of course, you can always check out the Ministry of Justice, Immigration Services Agency website for more info (https://www.moj.go.jp/isa/index.html) .