Under Canadian law, you are “married” if you have undergone a legally-recognized form of marriage, officiated by someone like a religious official, judge, justice of the peace, or other person with the needed authority.
In contrast, you are in a common law relationship if you and your partner are living together, without having undergone a marriage ceremony.
The law treats these types of relationship differently, in terms of your legal rights and obligations towards each other, if the relationship ends. Even so, once you meet the legislated threshold of having cohabited for a certain period of time, you do get the benefit of certain rights upon separation.
For more information, see this article: How Long Should We Live Together, to be Common Law in Ontario?