In 2018 the Supreme Court of Canada modified the legal definition of what it means to be "habitually resident" in a country, which Canadian judges must follow when ruling on international parental abduction cases. The Hague Convention is an international law which mandates that Contracting States must order the return of a child that has been wrongfully removed or wrongfully retained to their country of habitual residence (unless one of the exceptions applies).
A separation is when two people in a domestic relationship decide to end their relationship and live separate and apart. There is no official designation given to couples who chose to separate. However, you and your partner will need to figure out how to divide the life you have built together, keeping in mind you don’t qualify for the same legal rights as married couples.