There are different 'group' station definitions for routeing purposes, and for fares purposes. The two sometimes overlap, but this is not always the case.
There hasn't been a "Brighton Stations" concept for fares purposes since 1989 - tickets are issued to specific stations of either Brighton, Hove, or London Road (Brighton).
There is a "Brighton Routeing Point Group" concept for routeing purposes, which means that you can double-back between members of the Group for interchange purposes only. But this only applies at an intermediate part of your journey, e.g. if you were travelling from London to Barnham, you could double back between Hove and Brighton. Can't see a scenario where it would help given the current timetable but if, for example, London-Brighton trains were diverted via Hove, and Brighton-Barnham trains didn't stop at Hove, that's the kind of scenario where it might be useful.
Buying a season ticket from Brighton is, for most intents and purposes, going to give you the same validity as one from Hove. This is because season tickets are valid for unlimited travel, including break of journey at intermediate stations. The "3 mile rule" allows you to travel via alternative routes within 3 miles of the shortest route, and Hove is within 3 miles of the shortest route to Preston Park and northwards.
Also, when tracing a mapped route you can use any route to the next Routeing Point that doesn't involve doubling back, so Brighton-Hove-Wivelsfield would be fine even if it were more than a 3 mile detour.