A bimolecular reaction is always a second-order reaction, but a second-order reaction is not always a bimolecular reaction.
The most important thing to take note of is that molecularity of a reaction is a concept applicable to only elementary reactions, meaning non-complex. In a way, elementary reactions are basic and achieved in one step. Complex reactions involve intermediate steps before achieving the desired reaction.
Molecularity is equal to the sum of the coefficients of the reactants, so two reactants give a second-order bimolecular reaction. However, second-order reactions can involve more than two reactants especially in complex reactions.