New York and New Jersey were originally both part of New Netherland, which was a Dutch colony, not an English one.

They were conquered by the English in 1664, re-conquered by the Dutch in 1673, but ceded to England in the Treaty of Westminster in 1674.

New Netherland included New York, New Jersey, Delaware (after conquering New Sweden in 1655), most of Connecticut, and parts of Pennsylvania and Rhode Island. (Though, by the treaty of Hertford, in 1650, New Netherland ceded control of their claims in Rhode Island, most of Connecticut, and the eastern end of Long Island to the English.)

After the English took over New Netherland, they split it into several colonies. New York was named after the Duke of York, who organized the expedition in 1664 which took New Amsterdam (New York City), rather than the English city or county (though the Duke was named after the English County). The Duke of York (later King James II) was the proprietor of the colony of New York.

James II then gave some of the colony to two friends who had stayed loyal during the English Civil War, Sir George Carteret and Lord Berkeley of Stratton. They named this colony, New Jersey, in honor of the island of Jersey (which was a Crown Possession but not part of the Kingdom of England) having remained loyal to the Crown throughout the English Civil War. (Charles II was proclaimed King in 1649 in the Royal Square in St. Helier, Jersey).

Delaware was leased by James II to William Penn, but he never merged it with his colony of Pennsylvania. The two colonies shared the same governor until 1776, but had different legislatures siince 1701.

Delaware was named after the Delaware River, which was named after Thomas West, 3rd Baron De La Warr, the first colonial governor of Virginia.

New England always meant the colonies of Plymouth Plantation, Massachusetts Bay (which included Maine, and into which Plymouth Plantation was eventually merged, to become Massachusetts), New Hampshire, Rhode Island, and Connecticut. Later the State of Vermont (which had previously been disputed territory between New Hampshire and New York, then, briefly, an independent Republic, before being admitted as a State) was included in the general term, as was the State of Maine, after it became independent from Massachusetts.

New England specifically refers to those colonies which grew from the original Plymouth and Massachusetts Bay colonies. So Maine, Connecticut, Rhode island, and Vermont were all former in one way or another from the original Puritan companies.

NY and NJ were acquired later from the Dutch having been previously part of New Netherlands and had much deeper ties to fellow middle colony of Pennsylvania.