'Academic work ' is work done: 1. As part of your studies - at college or university for instance. 2. It also usually includes work done while you were employed to teach, advise, or research by an academic institution. 3. It also includes work done by yourself (when not employed by anyone) solely for the purpose of publication in an academic journal. Professional work is paid work outside of the academic world. A private company for instance, OR paid work while you are self-employed. If you personally did research, I would include it as 'academic' if the work involved publication, or the work involved a college/university in any way. Otherwise, if it is personal paid work (contracts) then it is professional. All other cases ....personal interest, charity work ... I would consider it as 'personal'.

Your understanding of "academic" and "professional" sounds correct to me. I'm not really sure about your research. If it wasn't for school or academic then you can probably classify it as "personal", but I would contact someone from the organization to which you are applying to get more information. It sounds like "personal" is being used to describe a "creative work" you did that was not for school or for a job. Maybe something like a design you made in your own free time.