The thirteen colonies were the ones that seceded from Britain, yes. As well, it's worth pointing out that, at the time, "Canada" was the colony where Ontario currently sits (more or less). There were a number of other colonies at that point, including Newfoundland, Prince Edward Island (or Ile St-Jean), and the Nova Scotia/New Brunswick colony, which was also known as Acadia (some times, and included Prince Edward Island, at times; the borders and names in the Maritimes are a bit complex during the 1700s, in part because of the British and French fighting over them).

The colonies that eventually became the country of Canada remained part of the British empire (not everyone in those colonies wanted to, of course, but the majority did; Nova Scotia certainly had a group that wanted to join the United States, especially in Yarmouth county). However, the Atlantic Canadian colonies were subject to a fair bit of privateering from the US, which wasn't met too kindly (to be fair, Atlantic Canada responded in kind with its own privateering).

There was some hope for Québec to join, particularly since it had fairly recently come under British control and, being a French colony originally, and mostly filled with French colonists, there was distaste for this, as well as fear of losing their culture. Most people, however, were either neutral or indifferent; this was followed by an attempted invasion in September 1775, by General Richard Montgomery. They took Montréal, while Benedict Arnold set out for Québec City. Montgomery joined him, and they attacked there in December; they made some headway, but were beaten back, taking only some of Lower Town.

They remained in the City, attempting a siege, but the spring brought British reinforcements, and they withdrew, abandoning Montréal in May. This invasion, along with its failure, turned Québec (and the other colonies') sentiment in general against the US cause.

So, the thirteen colonies refers to those that are part of the United States, that fought to secede from Britain; "Canada" is comprised of several different colonies, isn't part of the US, and didn't secede until later, forming a separate country, and doing so peacefully (through various necessities). US sentiments weren't particularly helpful for getting Canada to join (the aforementioned invasion, the War of 1812, the Civil War, and the "Manifest Destiny", among others things, serving to turn general feeling against such union). As well, the influx of Loyalists following the War of Independence brought many who were against joining with the US when its independence was recognized in 1783.

You can read more on the thirteen colonies here, though the parts on Canada and its colonies are rather vague.

A bit of Canada's history during the War of Independence can be read here, though it's a bit light.

On the War of Independence's affect in Canada, especially in Québec, you can read here.