No, New Jersey was one of the original 13 proprietary colonies. These colonies were all English colonies.
New York was actually New Netherland to start but, most of the 13 colonies were formed for the basic reason of religious freedom.
The Dutch colony of New Amsterdam became the English colony of New York.
New York
Vermont is not one of the original 13 colonies because it wasn't English land! It was actually French and the name Vermont means Green Mountain in French.
The original purpose of starting New York colony was to expand. This colony was started by the Dutch as a business endeavor.
New Jersey
the English name for the Mannhattan colony was New York
New England colonies
New York was an English colony because the English conquered New York from the Dutch, and after ceding to the English in the Treaty of Westminster, in 1674.
New Sweden was the original nae of Delaware Colony. Delaware became part of three English colonies: New York, Maryland, and Pennsylvania.
Originally New Amsterdam a Dutch Colony it became the English Colony of New York.