They go hand in hand - to figure out the equilibria, you have to propose strategies for each player and play them out to their logical end. The optimal strategies (which are not necessarily winning ones, e.g., if everyone loses), are the ones that lead to equilibrium.

Equilibria and strategies go hand in hand. To figure out the equilibria, you have to propose strategies for each player and play them out to their logical end. The optimal strategies (which are not necessarily winning ones, e.g., if everyone loses), are the ones that lead to equilibrium, precisely because no one has the incentive to change strategies.