There is only one category of Schengen short-stay visa, namely, the type C short-stay visa. In applying, you must justify the purpose and conditions of the visit, which may be a business visit, a tourist visit, or indeed nearly any other kind of visit. In your case, of course, the justification is a business trip; in the case of your family members, it is to accompany you while you are on a business trip.
In countries that do have distinct categories of visa for business and touristic visitors, it is common to grant tourist visas to family members accompanying business travelers. It is also commonly recognized that business travelers will engage in touristic activities during their free time.
In short, your family members should just apply. If asked to categorize the purpose of the visit from a list of choices, then they can choose "tourism" unless there is another choice that describes their intentions more accurately.