Generally, one is considered a part of the other - and yes, in both directions. The real difference is in theory versus practice - in practice, there is no such thing as a completely free market, nor is there completely free trade. The two - free markets and free trade - are ideals that presume no negative externalities, but it's the externalities that drive governments and policymakers toward conditions that are less than fully free, in markets and in trade. (That's a good thing, by the way.)