The biggest difference between lacrosse and field hockey is that field hockey is played with a stick with a curved end for pushing the ball, while lacrosse requires a stick that has a net used for throwing and catching the ball. Another difference is that the goal used for field hockey is much bigger than the one in lacrosse.
Field hockey balls are slightly larger than the ones used for lacrosse and weigh slightly more. Additionally, field hockey is a non-contact sport while lacrosse is usually played with contact. In lacrosse, the game is divided into four 15-minute quarters, with a half time after the first two quarters, like American football. Field hockey is more like soccer, with two 35-minute halves divided by a five- to 10-minute half time. Other similarities between field hockey and soccer include "corners" being awarded if the ball goes over the back line of the playing field (which is called a pitch, as in soccer) if last touched by a defender, and penalty shots being awarded for defensive fouls occurring within the scoring circle.
Interestingly, lacrosse has been played in some form since the time of the first European contact with Native Americans and it is similar to many other stickball games that were played by indigenous peoples all over the Americas.