Your relative gave a records clerk the name of the village in Europe where he or she was born. The records clerk did not know how to spell the name of the village. Your ancestor might not even have been certain how to spell the name of the village. The records clerk was unfamiliar with where your ancestor was from. The clerk simply spelled the word your ancestor gave him as best the clerk could spell it.
So your German ancestor’s village of birth got spelled the way an English speaker thought it should be spelled. If you are having trouble finding a village, you need to think about the way the word that was written was said. Then try and discover how that would have been spelled in your ancestor’s native language.
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Case in point: documents say Reckzien and Reckzin Germany. On an old map I found Rexin but still not sure. The Meyer Gazzateer is a good tool for these problems.