This is a confusing issue in most common law jurisdictions and AFAIK, Canada and Australia still rely on common law definitions of this.
First, any arrangement where someone provides services in return for compensation is a contract. If worker is an employee then the contract is an employment contract and is subject to whatever laws apply to employees (things like, workers' compensation, withholding of tax, superannuation etc.). If the worker is instead operating their own business that is independent of the principal's business they are independent contractors and employee law doesn't apply.
In most cases it is easy to determine if someone is an employee or is a contractor. For example, if your business hires a bookkeeper to work set hours for which they are paid a salary from which you detect and remit tax, etc. then they are clearly an employee. Your external accountant who does your year end taxes, has their own premises and contracts to many other businesses is clearly an independent contractor. However, the dividing line is not clear cut in edge cases.
Using British Columbia as an example:
Calling a person an independent contractor, even if the worker agrees, does not decide the issue.
In order to determine whether a worker is an employee or an independent contractor under the Act, it is important to consider the definitions of “employee”, “employer” and “work”. The Act defines these terms very broadly.
The courts have developed some common law tests that may be useful, but they must be considered in a manner consistent with the definitions and purposes of the Act.
Some of these tests include how much direction
and control the worker is subject to, whether the
worker operates their own business and has their
own clients, whether the worker has a chance of
profit or a risk of loss, whether the work they are
doing is integral to the business and whether there
is an ongoing relationship.
The longer a person works for another, the more
closely the worker’s duties are connected to the
purpose of the business, the more the person who
pays the worker controls the material and tools and
directs the activities, the more likely it is that the
relationship is one of employer/employee.
So, deciding if a person is an employee or contractor is not up to the worker or the principal and what they may or may not have written on a piece of paper! The entire relationship must be considered.
As an additional complication, legislation is not uniform between state/provincial and federal levels of government and even within the same jurisdiction. For example, in Australia, it is possible that a person is an independent contractor for Federal income tax law but an employee for state workers' compensation law.