The ultimate in proof that you've done research is that you are an author on a paper about the generalizable new knowledge you've generated by your systematic investigation.
Even if you don't get a publication, you might propose something called "research" (most often this means proposing a set of experiements to test a hypothesis -- this is called submitting a research proposal) and get someone to agrees to provide the resources needed to conduct the research. This is called "getting funded". Most often the PI gets funded and passes some of the resources down to you but some students are funded through student research programs. Sweet.😀
As a volunteer or as part of a class you might run experiments that are needed in the bigger scheme of things to test a hypothesis or generate new knowledge or serve as pilot data for a research proposal. You will be making systematic observations and sharing those observations with others. That is research.
Now there is some work in the lab that does not involve systematic observations such as washing glassware, making solutions, and stocking shelves. This is called "housekeeping". Some volunteers do nothing but housekeeping. Life is better if everyone does a little more than there share, just like in a regular house. Housekeeping is not research. You should aim to do some housekeeping because that is part of being a good citizen of the lab but you should not get yourself into a volunteer position (at least not for the long haul) where you do nothing but housekeeping.
