clairobscur, this is one of the differences between labour law in North America and in Europe. The U.S. Wagner Act (which was the inspiration for most of the labour relations laws in Canada as well) relied on the concept of a bargaining unit. A union that wants to organise a group of employees at an employer signs them up, and then applies to a government board (at the federal level in the U.S., the National Labour Relations Board, if I remember correctly) to have the work unit of the employer certified as a bargaining agent. The employer has a right to make representations about the appropriate bargaining agent.
The idea was that certification of a bargaining unit would increase the rationality of the union system, by putting all the employees who are doing similar jobs in the same bargaining unit within the employer. So for example, if an airline is unionised, all the pilots for that airline will likely be in the same bargaining unit. For a smaller employer, that means that there may only be one or two bargaining units; for a large, national employer it may mean that there are a variety of bargaining units.
Normally, if the Board certifies the bargaining unit as proposed by a union, the Board also certifies that union as the bargaining agent for that bargaining unit, but that recognition is not in perpetuity. The labour relations laws normally recognise an open season (usually every three years or so), in which another union can apply to be recognised as the bargaining agent for a particular bargaining unit, if it can show that it has majority support among the employees. Alternatively, if the employees are dissatisfied with their union, they can apply to the board to have their union decertified, without necessarily proposing a new union to represent them - i.e. - they can vote to de-unionise.
There are also laws regulating the relationship between the union and its members - one of the most important is the duty of fair representation. If an employee believes he/she has a grievance against the employer (unfair allocation of overtime, etc.) under the collective agreement, the union has a duty to represent that employee by raising the issue with the employer under the dispute resolution mechanism of the collective agreement. Since the union has been certified as the bargaining agent for all the employees in the bargaining unit, it has a corresponding legal duty to represent them all fairly in matters within the scope of the collective agreement.
Lots of qualifications on this sketch - it’s been several years since I studied the issue, and am certainly open to correction if I’ve got anything wrong.