There is a relatively pareve explanation for the separation between Pinsk Karlin and Karlin Stolin. When the Rebbe R’ Yochanan Perlow was nifter in 1955 or so, his desgnated successor, his grandson the current Stoliner Rebbe, R” Boruch Meir Yaakov Sochet of Givat Zev, was all of 6 months old. Those who didn’t want to wait for him to grow up formed a breakoff group and called it Pinsk Karlin.
Yes, I know that there’s more to it than that, but that is a relatively harmless version of the story.
The Loitzker Rebbe is R Yochanan Sochet, younger brother of the current rebbe of Karlin Stolin. Young enough to have been named after his grandfather, R Yochanan.