my favorite teacher in my old school taught us that there are two different types of scholarships. I'll call them "science" and "arts" although I'm not sure if that really fits. basically, everything that is based on nature is science, everything that's not is arts. He also said it's not a clear distinction, and there are people who claim that almost everything is science. For example, astronomy is clearly science, and astrology is probably arts. However, you could make the argument that even astrology is science because it's based on things in nature, and likewise, many scholarships that are widely considered arts are in fact science. He concluded that the only scholarship which is clearly not science is maths, because it is purely based on definitions. That always made sense to me.
The translation is iffy here though. In german, there are three terms:
Wissenschaft, which is translated science
Geisteswissenschaft, which literally means "science of the mind" and which I translated with arts, and
Naturwissenschaft, which literally means "science of nature" but which is used as a synonym for science.
So everything is called a science, it's just a question of what kind of science it is. The distinction in this case is between the latter two.
well anyway, I do think a distinction exists here. The English terms seem unfortunate though, because why should maths not be a science just because it's masturbatory. unless that's the kind of definition people have for science.