A penalty kick is awarded for a serious infraction of the rules -- offside, foul play, etc. A free kick is awarded for a more technical infraction -- the most common cause is probably an early engagement in the scrum. There are two major differences. (1) A free kick cannot be used to take a direct kick at goal. The ball must go through at least one phase of play (ie a tackle) before a drop goal can be attempted after a free kick. A penalty, however, can be teed up and kicked straight at goal for points. (2) If a penalty kick goes into touch, the kicking team retains the throw into the lineout, at the point where the ball went into touch. A free kick, however, is the equivalent of a kick in open play. If a free kick bounces into touch the non-kicking team gets the throw in, and if the kick is directly into touch and the kicking team is outside of their 22 metre line, then the usual rule applies and the lineout comes back to the point where the kick was taken from.