The "far side" is the part that never faces the earth (the moon is tidally locked, we always see the same side of the moon.) The "dark side" is, well, whatever side is dark to us. So when, for example, we have a "new moon" (where there's no moon at all) the side we normally see is dark but the "far side" is lit... to no one's advantage.
But on a pure basis of just every-day, layman, talk saying the "dark side" is probably enough to get the message across you're talking about the "far side" of the moon we never see.