score:2
For the VFS site, which you report requires you to choose "tourism" or "business," I would suggest that you choose "business" because an internship is closer in nature to a business visit than it is to a tourist visit.
When you get to the application form, however, you will be using the standard Schengen visa application form because you will be applying for a short-stay visa. There are many more options for "purpose of travel" aside from just "tourism" and "business":
You could reasonably choose cultural, but if I were completing the application form I would probably choose other and write "Erasmus internship."