There seam to be some confusion about "permit" and "visa".
A visa is a stamp in the passport which allows to initially ENTER the country. Some nationality need always a visa, some only if they want to work or stay longer than the 90 days in any 180 day period, and some nationalities do not need a visa at all.
There are two major types of visa: The Schengen Visa C, which is for short stays up to 90 days in any 180 day period, which might allow a single or multiple entry into the Schengen area, and the national visa D which is used for longer stays. The visa C is issued based on the common Schengen rules, while visa D is issued based on the rules and regulation of Switzerland. A visa D can usually only be issued if there is a pre-approved permit
A permit allows to work, study, or stay longer 90 days. Non-EU/Non-EFTA nationals need a pre-approval, EU/EFTA national can usually get one by simply registering their residency (if the fulfil the conditions of the FMOP).
To add further confusion, the English language is not very precise and the term "permit" is used for two different things: once for the actual permission (in German Aufenthaltstitel), and second also for the physical card (German: Ausländerauseweis, which means foreigner ID). The permit card shows that the corresponding permission permit exists. It is like a passport or driving license which shows citizenship or the driving privileges.
A permit might be for residency only, for work with a specific employer only, or allows any kind of work . The physical permit acts as a visa substitute for entering Switzerland and the Schengen area, and one can travel as a tourist up to 90 days in any 180 day period in the Schengen area. The most important permits are permit L (short term residency up to 1 year), B (residency), C (permanent settlement), and Ci (family member of diplomats and members of international organization with regular gainful employment). ( All permit types: https://www.sem.admin.ch/sem/en/home...ufenthalt.html )
A permit is usually issued based on a reason, such a work, study, medical, pensioner, family reunification, diplomacy, the FMOP (Free movement of person agreement with the EU), etc.
Procedure for family reunification:
Only Swiss and EU/EFTA nationals have a right do bring there extended family to Switzerland. Non-EU/EFTA person , be it on permit C or B, can normally only bring spouses (by Swiss law their a person can only one spouse) and their children. See chapter 7 FNIA and Annex I Art. 3 FMOP .
To get a permit for the family members you must have enough living space, the finical means. If this is fulfilled, you make an application for family reunification with your cantons immigration office. If approved the relative can apply for a visa D at their usual place of residence ( if a visa is needed ). Once the visa stamp is in the passport they can move to Switzerland ( see customs information ), register their residency which activates the pre-approved permit (the permission), wait for invitation to take biometrics for the permit card, get biometrics taken, and wait until the permit card arrives. The permit is usually a permit B which allows to take up any work. (Exceptions apply, such as for children under 12 which will get permit C if the parents have permit C. The restrictions for Croatian nationals no longer apply).
tl; dr; One does neither apply for visa nor permit but simply for family reunification. If approved a permit B and a visa D (if needed) is issued.