Sometimes where a person was born can change around them, when they live and die in the same house in which they were born.
Sometimes those different places of birth can be because someone, sometime, mixed up different people with the same name.
Sometimes it can be because the person giving the information didn't know, so made a "best guess" (maybe it was a neighbour talking to the census taker, or a child).
In the case of immigrants, mostly it's because the geo-political borders had been redrawn several times - as in parts of Europe - so someone born in a German State that was before a unified Germany is suddenly born somewhere they wouldn't recognise.