To my understanding, in Canada, an employee is given more protection and entitlements under the law, than a contractor. What would go into proving one is an employee and not a contractor? Would this be akin to "suing the employer in court"? Which court or tribunal would it be brought to? Does it not make a difference if a person is a contractor or employee until a dispute arises and it becomes unclear which laws (e.g. labour laws) apply?
Raise the question with your employer
If you believe that you are an employee and not a contractor then there is presumably something you want from your employer. This may be additional wages and entitlements that you would have or will become entitled to for past or future work respectively. Or you may have been injured and want workers' compensation. Or terminated and you want redundancy pay. Whatever it is, work it out and raise the issue with your employer. You might want to consult an accountant or union to help you.
They may acknowledge that you were incorrectly classified and give you what you want. Winner, winner, chicken dinner!
Or they may dispute it. If so, you need to follow the dispute resolution processes at your workplace. These typically involve informal discussions, escalating to mediation and then to a workplace tribunal run by the government. You will almost certainly want to consult a lawyer or union to help you - given that you don't know where to start the learning curve is likely to be too steep.
In virtually every jurisdiction if people are employees at law they can't choose not to be.
in british-columbia the relevant law appears to be the Employment Standards Act although it's not unheard of in edge cases for a person to be an employee under one law (e.g. workers' compensation) and a contractor under another (e.g. income tax).
From the linked site:
The overriding question is “whose business is it?” Is the person who is doing the work doing it as a person in business for themselves?
If you are working "for" your own business you are probably a contractor. If you are working "for" your employer's business you are probably an employee.
For example, if you are an accountant with several dozen clients, maintain your own business premises and charge for your advice based on the amount quoted rather than by the hour, you're a contractor. If instead, you have 2 clients, work from their premises at set hours and get paid by the day or week, you're an employee with 2 jobs.
In edge cases these are not cut and dried - Google are Uber driver's employees. In Australia: no. In California: yes. In the UK: yes.