During the colonial era before the American War of Independence, Britain sent convicts to its North American colonies which eventually became the USA, but did Britain also send convicts to those colonies which became Canada?
Yes. In 1730 and again in 1789, Britain sent convict ships to Newfoundland. However, neither experiment was successful as they found that St. John's could not incorporate the scores of new residents. There were scattered instances of a handful of convicts being sent to Newfoundland for seven-year terms, but no other large-scale attempts to export convicts to Newfoundland (or other Canadian colonies) seem to have been tried.
Eighteen colonies in America received around 50,000 convicts during the 18th century, but 90% went to Virginia, Maryland, and Pennsylvania. Why? The British government did not designate destinations for convicts, but instead contracted merchants to ship them out. Planters in those colonies paid well, plus the merchants could pick up valuable return cargo while they were there.
Though you ask specifically about Britain, it's worth noting that the first attempt to settle Nova Scotia involved a French convict colony on Sable Island in 1598.