The M in both names means different things - the PM manages is the product scope, the EM manages teams. Thus, most PMs are ICs, and EMs are people managers.
This, in turn, causes the experience needed to become a PM or EM to differ. Very few organizations would hire a new grad into an "Associate People Manager" job - it is implied that one needs some experience in the industry before one can be entrusted with people management duties. But many new grads step into "Associate Product Manager" roles, where they are on a career track to own business strategy. This is, IMO, a bad trend in PM orgs.
This imbalance in industry experience is often the root cause of tension between many PM/EM pairings, particularly in B2B space.