When two people who have been living together in a marriage, or a marriage-like relationship (sometimes called a common-law relationship), decide not to live together any more, they are separated.
There is no such thing as a "legal" separation. If you are living apart, you are separated.
It is possible to be separated and still living in the same home where a clear intention of a permanent separation has been communicated and acted upon.
For more information, see Going through separation on Legal Aid BC's Family Law in BC website.