Not quite. The Pinsk one is a break away faction of Karlin Stolin.
In short there was a break away (mostly) when the previous Stolin Rebbe zt”l was niftar and many of the Jerusalemite Karliners (mostly elders) saw no future Manhig within the Chassidus. So they turned to the Tzaddikim of Lelov, who were very close to them. The others (mostly younger generation) and those in America, waited on and accepted the leadership of the current Rebbe Shlita, who was young at the time. Needless to say this created a bit disharmony. This “arrangement” continued many years, until on fine day the Lelover Rebbe (forgot which one) decided enough is enough, and ended his leadership of the Karlin segment. Those stranded without a Rebbe chose for themselves Rabbi Aharon Rosenfeld as their Manhig. Originally they called themselves “Karlin”, after a ruling of Bais Din they distinguished themselves with the title Pinsk – Karlin.