It is not so much a difference in skills, but the philosophical approach that determines their use.

A physicist would primarily be interested in questions about what reality is and how we perceive it.

A mathematician would primarily be interested in how we reason about things: in abstraction and logic, in linguistic and non-linguistic mental constructs.

This difference in philosophy changes the kinds of questions one asks *and* the kinds of answers that are considered "satisfactory".

It also leads to differences in the aspects of the skills (be they computational, relational, spatial or some other) that one hones *even* when the basic skills are from the same set.

In summary, the difference is not so much in the skill sets, but in the value/onus placed by the "owner" of these skills on them. As a consequence, their use can be different.