The permit is the company’s; the confirmation is yours.
The разрешение authorises the employer: it is the company’s permit to attract foreign labour, issued by the Agency for External Labour Migration. The подтверждение authorises the person: the individual confirmation of the right to work. They are issued separately, to different holders, and each side of the employment needs its own — subject to the categories that are exempt from one or both.
Category, permit, invitation and visa — sequenced so the hire arrives when planned.
Part of the answer bank — 52 questions, each cited to the article it rests on.