The following is based on my experience as an amateur genealogist:
Poland Russia and similar hybrids usually refer to Suwalki, and sometimes to Kleipeda and White Russia (Belarus). Suwalki also bordered on Kongsberg--Alexotas in Suwalki was always regarded as a suburb. The general Suwalki region was contested between Lithuania and Poland, now mostly in Lithuania. However, census records sometimes refer to birthplace and sometimes to last residence, and the borders fluctuated over time. So, one has to be careful as to what the reference means.
Because of its border status, Suwalki was often a place of refuge for those seeking to emigrate to the West. So, a lot of families that originated in Vilna or Kovno (Vilnius and Kaunas) transited through Suwalki and were temporarily registered there. Occasionally, people from Grodno or even Minsk used the Poland Russia designation also--indeed, this was true of any region that had been part of the Polish-Lithuanian Commonwealth but was incorporated into the Russian Empire after the three Partitions.
In particular, the Kleipada (German: Memel) area (and further north into Livonia around Riga in Latvia) were frequently still called German by ethnic Germans long after these regions were acquired by Russia. (This was actually East Prussia but I seldom find this term in census records. Riga and Dwinsk mostly had ethnically German populations.)
So, the designation Poland Russia often depended on one's own ethnic background.
Sometimes, onomastic analysis combined with crew passenger lists from Hamburg can resolve these ambiguities.