[sushisource]

It's just about how it's colloquially used. Even in industry we mostly call ourselves software engineers / developers, but if people say "Computer Scientist", especially in the context, it's generally understood you didn't mean PhD level research.

Mathematician, OTOH, does kinda usually imply that, or at least implies you do something that likely requires beyond undergrad level education.

[ska]

Sometimes people differentiate by, for example, saying "research mathematician" but I think the meaningful distinction is: do you spend (an appreciable fraction of) your time creating new mathematics...