Generally the recalculation works like this: it takes your rating 15 games ago and looks at the results of recent 15 games and applies black math to it to get a new rating.
We have separate ratings (and other glicko parameters) for each category (16 categories in total).
So if you played 9x9 correspondence it’s going to change 9x9 correspondence, correspondence, 9x9, overall ratings. In each recalculation the rating algorithm is going to use ratings (and other parameters) for that category. And changes will be all different.
Imagine playing 9x9 with someone who hasn’t played 9x9 at all but played lots of 19x19. Since they have an established overall rating (from their 19x19 games) this 9x9 result will have significant effect on your overall rating. But in the category of 9x9 they have basically “?” rating and therefore the result won’t have a big effect on your 9x9 rating.
Essentially these categories are decoupled. Each category doesn’t know what other categories are doing and is doing rating changes on its own. Yes, they share some games but in practice these are very different rating systems. Kind of like comparing your rank on foxy and kgs.
You can refer to @flovo’s conversion tables, they show generally what rating in one category corresponds to in another category. They say if you look at the graphs for too long, you can see god.