This is off-topic but it is actually quite common in Westchester for towns to include incorporated villages within their boundaries. The Town of Greenburgh includes the villages of Tarrytown, Irvington, Dobbs Ferry, Ardsley and Hastings-on-Hudson. The Town of Eastchester includes the villages of Bronxville and Tuckahoe. The Town of Mt. Pleasant includes the villages of Pleasantville, Sleepy Hollow and
part of the village of Briarcliff Manor. The other part of Briarcliff Manor is within the Town of Ossining. The Town of Rye includes the villages of Mamaroneck (part of which is also in the Town of Mamaroneck), Port Chester and Rye Brook. The City of Rye is NOT within the Town of Rye. It's separate.
There are many reasons why this situation evolved as it has, none of which have anything to do with this forum.