When you take the two oldest sports in North America you expect to see some similarities. Lacrosse was invented by the Native Americans and when started was played as a war game which included hundreds of people at a time. The Canadian colonists saw this game played and created there own version starting a great game that features the oldest professional trophy in this continent. They are viewed today as the to most physical games out their and rightfully so considering the things involved like checking, slashing, and tripping. These "war" games appear fundamentally the same in many aspects such as rules, players and goaltending, but if you look closely they have many differences.
When comparing these sports, the first, and probably most important detail are the rules. Both sports allow very physical play, which makes for an entertaining game. An important rule difference between the sports is that in lacrosse slashing is aloud and a very important part of the game. In contrast slashing is a serious infraction in hockey and cause cuts and fractured bones. Penalty time is similar in both sports the way it's served and what happens during the penalty. In both sports, when on a penalty you play with one less man and the other team tries to work the puck or ball around the offensive zone to try to create an oddman situation. This is done to get an open man with a shot on goal and is almost identical in both sports. .
Player participation is another point to consider when comparing these sports. In hockey each team has five skaters and a goalie which is very different than lacrosse. Lacrosse is set up more like soccer in that you have forwards, midfielders, and defense as well as a goaltender. This creates a more ridged playing style where some players don't go all over the field. In hockey every player is a defensman when the other team has the puck and when your team has it everyone's on offense.