What is the difference of pure strategic equilibria and nash equilibria?

Question

Are they the same thing just named differently or with minor differences?

Answer 1

Nash equilibrium is (by definition) a profile (set of strategies - one for each player) on which every player descreases his payoff chaniging his strategy if all the rest players do not change their strategies.
Pure strategies are the strategies when every player chooses the same strategy each time. There are also mixed strategies when player has a set of probabilities defined for his strategies, so he chooses different strategies in different instances of the game.
Pure strategy equilibrium is Nash equilibrium containing only pure strategies for every player. All games have at least one Nash equilibrium but these equilibria might be only mixed equilibria (or Nash equilibria in mixed strategies).

Thus, pure strategic equilibrium is always Nash equilibrium (in pure strategies), whilst Nash equibrium is not always pure strategic equilibrium : it might be either pure or mixed strategic.