Perfect Bayesian equilibrium isn't just a subset of Nash equilibrium. In Perfect Bayesian equilibrium, players must believe their opponents are following the equilibrium strategies. In contrast, Nash equilibrium doesn't spell out these beliefs. However, in Nash equilibrium, players tend to assume others are sticking to the equilibrium strategies. This could lead to a narrower range of believed strategies than in Perfect Bayesian equilibrium. As a result, the equilibriums covered by Perfect Bayesian equilibrium don't all fit under Nash equilibrium.