No, the layouts do not have to be the same. In fact, having them different will allow you to move fields around or to add fields that are more appropriate for posted vs unposted.

For instance, fields that associated with the application process like paperwork requirements belong on the application tab, but once the grant is approved, don't need to be visible on the applciation history tab.  A field to record the grant outcome isn't needed before a grant is paid, but would be useful afterward.