Trying to understand administrative divisions in New York (County, Village, City, School District, etc.)

[Greg Baker]

Help!  I wanted to check out tax rates within some nearby areas and started out here: http://www.osc.state.ny.us/localgov/orptbook/2012t...

I was quickly baffled by the differences between counties, municipalities, class, school district, etc.  

After doing some reading here http://en.wikipedia.org/wiki/Administrative_divisi... and also googling images of county wide municipality, town, and school district maps I THINK, I have created a list of "truth" statements, and sketched out a visual to represent the relationship between counties, towns, villages, cities, school districts, and the term municipality.  

Please let me know if these "truth" statements are true.  I am working within the filter of New York State only, EXCLUDING New York City.

"Truths":

• Municipality is a governing unit, not a physical boundary
• States are the major division of the country
• Counties are major divisions of the state
• Towns are major divisions of the county
• Villages and cities are located within a town or towns
• Villages and cities are located within a county or counties
• All towns in NY are within a single county
• Cities and villages may or may not be named the same as the town(s) they are located within
• School Districts can span multiple counties, thus they can span multiple cities and villages

Visual Sketch:

Thanks!