Translation:I live in a small village.
I don't think so. No one in the USA would call where they live a "village" (apart from a few Natives, maybe). Only "town", no matter how small it is. Villages are only in the Old Country or occupied by indigenous people. On this account, I don't understand the difference in Japanese: is it a matter of size?
The technical definition of cities, towns, and villages in Japan is based on population. A city usually has a population of over 50,000. I'm not sure the definition for a village, but definitely less than 10,000. These definitions are not always strictly adhered to, but that's the basic gist.
While it is true that some places have "village" as part of their official name, I've never heard somebody use the term to describe it.
For example, my grandparents lived in The Village of Neshkoro, WI, but I only heard them (and everybody else) use the word "town" to describe it (specifically "small town")
What!? No way!
My mother was in the Navy, so I've lived my whole life here in San Diego, but I spent every summer until I was 18 in Neshkoro at my grandparent's house on Silver Springs Lake.
My family has been in the Princeton-Neshkoro-Wautoma-Red Granite-Princeton area for 5 generations now. Family names are Voight, Barclay, Greening, Polis... are we cousins?