Generally speaking, forced migration is a broader conceptual category. It would include refugees, including internally displaced people who do not cross an international border, including refugee claimants or asylum seekers who don't yet have their refugee claim, and also including people who are displaced for environmental or economic reasons, who would not be considered refugees under the UN convention but are clearly displaced involuntarily because of natural disasters or human rights abuses.
It's a very broad term, and refugees would be a subcategory of that. Refugees have a specific legal status under the UN refugee convention and under domestic law. In Canada, that would be IRPA.