Laic and laicist derive from the same root. Why did their meanings diverge? What meaning do they share? Both apply to people who believe that the well-being of societies requires that religious doctrines and churches do not interfere with the functioning of the state. To the laic, this end is reached when the state refrains from taking side with one confession against one or more other confessions, from supporting one citizen at the expense of another because of his or her religion. From an ideal—typical perspective, a laic state shows and practices neutrality between different confessions. To the laicist state, this is fine but not enough; neutrality between confessions is the goal, and state institutions have the responsibility to create egalitarian conditions. The state's job is to actively provide an environment equally propitious to believers in some God, agnostics, and atheists, and to stifle any attempt at endorsing confessional discriminations or church interference in public life.
Source: wiktionary