Air Passenger Protection Regulations apply to both large and small airlines. However, different requirements for compensation and rebooking apply to small airlines.
Large airlines are those that have carried more than two million passengers in each of the two preceding years (e.g., Air Canada, British Airways). All other airlines are small (e.g., First Air, Harbour Air).
If a small airline is carrying passengers on behalf of a large airline under a contract, they would have to follow the large carrier obligations for those passengers. This includes, for example, situations where a small airline is operating a flight, but some or all the passengers on the flight have bought the ticket from another large airline (code share or capacity purchase agreement).
Usually, the ticket and/or itinerary will show you which airline sold the ticket and which airline is operating the flight. You can tell who issued the ticket by looking at the first two letters of the flight number (these letters represent the unique two-letter code of the airline that sold the ticket).