To understand this relationship, lets first look at what each of these parameters are, how they are defined, and how they are used.
Application Name ( 'Application')
When you join the developers program, you are given a set of developer keys. The Developer Name defines your account, and is the same for Production and Sandbox. The Application Name defines a specific application you are creating. The certificate simply is a 'key' required when making API calls. A developer account can have multiple Applications, each defined by its own Application Name. Typically however, there is a one-to-one ratio between Application Name and Developer Name. All API calls you make are tracked by your Application Name.
An Authentication Token is tied directly to an Application and an eBay User. The token is not linked or tied to an Runame. The Runame is just a mechanism for determining the Auth and Auth settings and referring Application. Once a token is generated, there is no link to the originating Runame. Additionally, all tokens for an application can be generated using the same Runame.