The early colonial history of the New Haven area is all centered around New Haven. In 1638, Theophilus Eaton and John Davenport acquired a lot of land from sachems Momaugin and Mantowese. They founded the New Haven Colony, which, when organized in 1643, included Milford, Stamford, Southold (on Long Island), Long Island, and Guilford. Branford, which was organized in 1644, joined New Haven Colony the next year. New Haven Colony was its own separate government — separate from Connecticut Colony, until 1665, when King Charles II ordered them united. (At some point, Long Island and Southold passed over to New York Colony instead.) Presumably in recognition of the colony's separate beginnings, New Haven was made co-capital of Connecticut Colony.
So several of the towns mentioned in last week's question — Branford, East Haven, North Haven, and North Branford — were all initially part of the land purchased by Eaton and Davenport. Guilford, on the other hand, was settled by a band of puritans who traveled through New Haven to make their own land purchase; Henry Whitfield acquired Guilford's land from Shaumpishuh, the female sachem of that region, and joined New Haven Colony, rather than the other way around. Branford started as part of New Haven Colony, purchasing land directly from New Haven in 1644 and splitting off as its own town at that point. The border between Branford and New Haven was debated for some time, as residents of Branford settled in areas that were technically still under New Haven's ownership — and thus, East Haven was a section of land under dispute between New Haven and Branford until around 1674.
It was eventually resolved that the land that became East Haven — then called East Farms — was indeed part of New Haven. East Farms settlers started one of Connecticut's earliest iron forges and blast furnaces in 1655. When New Haven established its official borders as a city, incorporating in 1784, the borders included all of East Haven, Hamden, and North Haven. East Haven became its own town in 1785. North Haven and Hamden separated off in 1786.
North Haven as a settlement is quite a bit younger than East Haven — originally called the Northeast Parish, the land was granted by James Pierpont to the people living there in 1714, on the condition that they would build their own meetinghouse. They formed the meetinghouse in 1722. About half of Pierpont's original land grant is currently the North Haven Green.
North Branford, on the other hand, was settled within a few generations of its southern parents. The settlers of Branford stretched into the northern-most areas of Branford's borders — up to where Northford is now — in around 1692. The early farmers were disinclined to permanently settle so far from the center of town life, especially for the winter, so many lived in temporary shelters; the first houses were built sometime in the 1690s — in fact, a home from 1699 (the Howd-Linsley house) was added to the National Register of Historic Places in 1986. More people began to settle the northern area through the early 1700s, and by 1717, there were enough residents to petition for their own church — though there was plenty of debate over whether or not the settlement should be awarded its own full-time minister for some years. (They were initially granted their own pastor for the winter months, but expected to share during fair weather.) That pattern of petition and denial continued for some time — in 1799, residents petitioned to become their own, independent town and were denied by the Connecticut General Assembly. It wasn't until 1831 that North Branford became its own political entity.