The terms Innie and Outie are only used by Innies.
For all practical purposes, Outie is the half of life that Innies imagine for themselves outside the confines of the Severed floor at Lumon, rather than the actual life they are living. Innies refer to that aspect as 'their Outie,' whereas the person actually experiencing life without memories of work does not conceptualize their work half as 'their Innie.'
Outies may demonstrate some mild curiosity about the work the Innie does for Lumon, but generally seem uninterested about the work life experience in the company.
As the half of the Severed personality that gets to experience life in the outside world, the Outie possesses all control over the Innie, including having the final say about whether or not the Innie can resign from their job.
From the perspective of an Outie, an Innie is not a real person, nor is it truly a part of them; however, some do have a vague sense that if they were to quit their job at Lumon, they would be in effect 'killing' the Innie.