Predoctoral fellow
In the physical sciences, a predoctoral fellow ("pre-doc") refers to a researcher who has a bachelor's degree, but not a doctorate. As the name implies, predoctoral fellows often use their time as a fellow to develop their skills and resume before applying to graduate school. In natural sciences, predoctoral fellows are most often graduate students and PhD candidates engaged in research that have not yet defended their thesis in requirement to obtain their PhD. They differ from lab managers or technicians in that they primarily pursue research, rather than maintain the day-to-day function of a lab, and may have external funding to support their research or educational activities, but typically are also reliant on the support of a research mentor whose lab they work in.
In natural sciences a pre-doc is usually a student registered in a Ph.D. program. In Mathematics typically a pre-doc is again somebody already registered in a Ph.D. program at a host university to work together with a professor in a different topic with respect to his/her topic.