Right now they are linked by government, but I really hope they will ditch that part, mostly because it's broken right now (for example, Hudson is favoured by non federal governments and aisling is favoured by non imperial governments). Right now BGS affects triggers mostly.What I've never understood about PP is its relationship to BGS.
If I work on a station, perform mining missions, improve the situation in this system and it somehow does not affect the PP ?
I always have the feeling that BGS and PP do not affect each other.
Other things current Powerplay affect is security levels, commodity availability and prices, module prices.
But again: I think it's useless to talk about CURRENT Powerplay, this seems to be something completely new, some things will probably stay but we have no informations about that, only speculation.