Was there a clear cultural/political difference between the thirteen colonies of America and the British colonies in Canada before the revolutionary war? Or was "Canada" simply the group of colonies that didn't rebel?

In short, yes. The regions that would be the US and Canada then were not much like the US and Canada we know now, and in some ways far more different.

A few things to bear in mind, that I think address your question:

Canada (here I mean what would be Upper and Lower Canada, now essentially Ontario and Quebec) had only recently been officially acquired by the British from France in 1763, at the end of the Seven Years’ War (known in North America as the French and Indian War). By this stage the 13 Colonies had a somewhat unified (if diverse) culture, already distinct from that of Britain, dialectal similarity being one measure of this.
Canada’s settler population in mainland Canada still consisted overwhelmingly of Catholic French Canadians, differing from the majority English-speaking Protestants of the 13 Colonies both in language and religion. The vast majority of Anglo-Canadians arriving after the American Revolution, the core coming from American loyalists who fled north in the wake of that very war.
This might depend on what you mean by ‘Canada’ at the time. Some of the Atlantic provinces (then colonies) were conquered by the British earlier, but most would join Canada in the latter 19th century, and Newfoundland only in the mid-20th, though they were considered quite separate at the time. These had mostly been French Acadia (apart from Newfoundland) but had been expelled over the first half of the 18th century (many forming the Cajun ~ Acadian population of Louisiana) had come in the gap between the wars, and some British and Irish settlers had come in in that time, including a largely Scottish Gaelic-speaking population fleeing the Highland Clearances in Nova Scotia. These had quite different cultures from the older and very English-speaking 13 Colonies, and though there was certainly trade (and competition over thinking) with New England, were geographically quite disconnected from them, and too small to rise in rebellion with them. Newfoundland was particularly separate, with an isolated and overwhelmingly fishing population that was Britain’s oldest colony outside Europe, and to this day has an extremely distinct variety of English (at least among traditional, often older people) which, unlike most varieties of American and Canadian English, does not fall in the same American English dialect continuum, but differs phonologically on most of the key defining points and sounds much closer to West Country English in some aspects and Irish English in others (varying in extent between these across the island). That said, Nova Scotia also included settlements of New England Planters, who moved up after the last major Acadian Expulsion in 1755. This and the Gaelic population may have been the one ‘Canadian’ colony ripe for joining the rebellion, but as a slightly more distant island they were far easier for Britain to maintain. No separate rebellion did erupt there, which would have been far more easily quelled than that in the vastly more populous connected collection of 13 colonies, though a delegation was sent to Washington during the war. He however refused to take action unless the Nova Scotians rose up en masse, as he felt this would amount to an invasion rather than a justified rebellion. Lastly, New Brunswick and Prince Edward Island had very small populations, some from New England and some from Britain itself, and also very recent (PEI in fact was only separated from Nova Scotia in 1769, six years before the war broke out).
Canada’s main areas of settlement were nowhere near the main areas of American settlement, being largely along the Lawrence River and Atlantic islands, rather than down the East Coast. We think of Michigan/Ohio and Ontario as close to each other now, but there was hardly any Anglo-American settlement even on the ‘American’ side at that stage: no Detroit, no Chicago. Certainly no Seattle or Vancouver yet, long before either country expanded west. They were still effectively very distant regions.
The French Canadians didn’t trust the rebellious Americans any more than they trusted the British Crown, in fact far less. The British Crown was a distant power and had formally granted them protections as new subjects, including their right to worship freely. Meanwhile, the French Canadians remembered how American colonists like Washington and others - les Bostonnais, as they called them all - had led the invasion that conquered them, treated them badly during the war, and included a lot of radical Protestants who saw Catholics as some Satanic enemy, especially but not solely in New England. The Second Continental Congress, with its declarations on fundamental freedoms, specifically tried to address this and sent out tracts to be given to French Canadians, but the majority were not convinced. Besides, they (probably correctly) saw the colonists as near enough to interfere more in a new North American state but too far away to offer immediate assistance should the British try to crush any Canadian rebellion.

So in short, it wasn’t that Canada was simply ‘the bit of British North America that didn’t rebel’, but that they were largely of a different language and religion and far more wary of the revolutionaries, or from a very separate British colonial tradition, and all much further away. But the core of mainland Anglo-Canadian culture as we know it came from American people who didn’t rebel: loyalists who moved north. Nova Scotia is almost an exception, though it had a small and separated population, but not to enough of a degree, and practical concerns and a lack of will won out there.