This is a really common problem, so I thought I'd write some more about how I have approached it in my own research.
First: you need to know where your immigrant ancestor really came from, not just where they sailed from. Some places to look:
- Passenger lists (sometimes give a place of origin), as you found
- US naturalization applications (sometimes give the exact birthplace)
- US WWI and WWII draft cards (ditto)
- US census records (usually only say the country of birth, but see below)
- Obituaries (occasionally give the exact birthplace)
If not your own ancestor, you may find one or more of those for your ancestor's siblings. My great-grandfather was one of twelve children and the only clue to his family's origin was one obituary for one of his brothers. My great-grandmother said she came "from Hamburg" but her brother's naturalization application had the correct town in what is now Poland.
Second: both the maps and the names have changed a lot in Germany and Poland over the centuries. You need to know what your ancestor's town was called, and what country it was in, for (at least!):
- the time they lived there, because that's how they will remember it and that's what the original records will say when you find them
- the time(s) they were asked, because that may be how they answered at the time and/or how it was recorded (e.g., by a census taker)
- today, because that's where you'll need to look
My 2nd great-grandfather gave all of these answers for his birthplace in these US Census records:
- 1850: "Germany"
- 1860: "Prussia"
- 1870: "Prussia"
- 1880: "Wurtemburg"
- 1900: "Germany"
His birthplace obviously didn't move, but its country kept changing around it! And the combination of Prussia with Wurtemburg turned out to be a helpful clue.
In my earlier two examples, my great-grandfather's brother's obituary gave his birthplace as "Danzig", which today is the city of Gdańsk in Poland; my great-grandmother's brother's naturalization application gave his birthplace as "Hohensalza", which I had to Google and learned is now the town of Inowrocław in Poland.
Third: the differences in German and Polish names and languages are noticeable, which can help if you get at least familiar enough to "feel" which is which.
My great-grandmother gave her maiden name as "McCaulskey". Yes, she spelled it like that. Yeah, nooo, it's definitely not Irish, nor Scottish, nor German. If you know what the Slavic languages sound like, you'll "hear" it: Michalski, which turned out to be her stepfather's surname and an important clue to identifying her birth family in the US.
Fourth: in areas that changed hands throughout history, ethnic groups often intermarried, so don't look for just the one whose surname you know.
My great-grandfather's surname was Rehbein, which is German. We were told that his mother's middle name was "Gazella", but I noticed some of the family's neighbors in Wisconsin had Gazella as a surname. Turns out it is a Polish surname, which our family didn't recognize because we were looking for Germans. Later on, I found that grandmother Gazella's mother was surnamed Schröder, which is German, so her parents were a mixed marriage too!
Fifth: keep checking back. In the last few years I've learned about two new projects to bring old Polish records online (there are many more! these are the ones I used):
- Pomeranian Genealogical Association (PTG), where I found my great-grandfather's parents' marriage record (matching the answer they gave on the 1900 US census), his siblings' and his mother's baptism records (all matching the data I had on them in the US), and her parents' names.
- Poznan Project, where I found my great-grandmother's parents' marriage record (matching her mother's US obituary), which gave me the name of their parish, Góra, so I could search for other records.
Sixth: some records were kept by the state, but you may have better luck researching individual parishes. In German areas, the difference between Catholic and Protestant ("Evangelisch") can be helpful when sorting out families (which will tend to be all one or all the other). In Polish areas, I have been surprised by how many parish records survived WWI/II. (Jewish research is different - a whole 'nother skillset which I do not possess.)
Using good old FamilySearch, which has tons of parish books imaged but not indexed, instead of searching for Records, search their Catalog for the parish you want. If you find a parish record book, you'll have to navigate the language and the handwriting and read through it page by page. (Google the terms - there are resources online to help you decipher.)
Seventh: as you've discovered, there are often multiple parishes in totally different regions with maddeningly the same name. There are several called Góra, which is why it was so valuable for me to know that the one I wanted was in Inowrocław.
And all of that is how I finally found my great-grandmother's baptism record!
Good luck / viel Glück / powodzenia!