First a disclaimer: I have found it hard to track down the oldest known actual reference to the fixed expression ‘Thirteen Colonies’, but they were the 13 colonies that were founded over the first century by the early 18th century: more specifically, New Jersey was united by 1702. To complicate matters, the Carolinas were united in 1691 and then split again in 1708 and more formally in 1729. Finally, Georgia was founded in 1733. From then until the Seven Years War of 1756-1763 (or ‘French and Indian War’ in North America), these were the only British continental American colonies, and the actual extent of those colonies (regardless of their political division and thus actual number) largely lasted most of a century up to that war.

The colonies in the Caribbean (and to an extent Bermuda) had a very different character: these were small islands where the British colonists (mostly wealthy and more connected to British aristocratic culture) were a minority, and the majority were African slaves forced to pick sugar and other crops, and who had a horrific death rate. The British Navy was also able to defend them effectively during the Revolutionary War, the only threats being the French, Spanish and possibly Dutch, so they were certainly not going to be included.

Officially, the British North American colonies fell under the colonial office of the British government (which despite mergers and splits, essentially continued until the mid-20th century fall of the British Empire). Being separated from England and then Great Britain by the Atlantic Ocean in days when transport was slow, many aspects of culture, including language, diverged from Britain but transmitted across these colonies: we can trace specific vowel shifts and parts of the lexicon to the 18th century, though many differences between British and American English postdate this. Language is a good first evidence of a closeness of culture, and the colonies certainly felt united by the time of the War of Independence.

I’m going to assume that you’re asking why those other regions under British rule when the American Revolution broke out were not included in this group: what are now eastern Canada (much of Ontario, Quebec, and the Maritime Provinces), the territories just to the west of what would be the US, and Florida (technically then West and East Florida). The first stayed under British rule, the second were transferred to the US, and Florida was returned to Spain.

Well, Canada was a very different place, and its population was not at all closely connected either geographically (mostly living on the Lawrence River, Nova Scotia, Newfoundland, and what is now southern Ontario). The vast majority were French Canadians, and had a very different culture in language (French), religion (Catholic), and political inclination (even if they were not overjoyed about the British government, they remembered that it was Washington and American colonists - ‘les Bostonnais’ - who had traipsed across them in the French and Indian War and before, and saw the New Englanders especially as Protestant extremists who might be both more inclined and nearer and thus more able to overthrow their own semi-autonomy and Crown-granted religious rights, so had no desire to join the Revolution). The first major Anglo population in Canada was made up of American loyalists from the 13 Colonies who arrived in the wake of the war. Above all, Canada had only just been officially absorbed by the British in 1763. They were not comparable. Similarly, there was limited Anglo settlement in the Floridas, which had also only just been officially British-ruled since 1763.

The territories to the west were in many cases taken from the French in 1763 too, and otherwise were not officially colonies but rather a buffer zone in which the British gave the Native Americans effective autonomy and rights protecting them from Anglo settlement from the 13 colonies to the east, one of the grievances strongly implied in the Declaration of Independence.

So as the American Revolution geared up, it was quite natural for Americans to see the 13 colonies as a connected group that needed to unite - but no more than those 13, though attempts to persuade the Canadians to join were made, in vain: the Second Continental Congress issued a declaration that (overwhelmingly French) Canadians who joined against the arguably common British enemy would be granted religious freedom, and tracts were printed and sent north of the border. But they were certainly not seen as part of the same cultural sphere.