Is PRINCE2 equivalent to APM?

No, PRINCE2 is not equivalent to APM. PRINCE2 is a project management methodology which describes who is responsible for what, and when within a project. It does not describe how to do these things. In contrast, APM is based upon tried and tested project management principles and practices that describe how project managers can plan and manage projects effectively.

PRINCE2 offers a certification scheme at Foundation and Practitioner levels. APM also offers several certifications, the most popular being APM PFQ and APM PMQ.