If you do a search on this subreddit you can get at the nuances of how gladiators fought and what the tactics of the legions were through out the life of the Roman republic and empire. But in general the most distinct difference is that gladiators were largely fighting by themselves whilst legionaires were part of a unit.

Gladiators were very much trained for an open fighting style with just one human or several animal opponents. They had specific weapons and armor to accompany their fighting style which was then often paired with a different style fighter. Fights were first and foremost for entertainment so you wouldn't actually be seeing many expensive and wasteful fights to the death as seen in movies.

The Roman soldier was alternatively subject to much stricter combat restrictions. Stay in formation in close order and don't break out to go chase down individuals, that will get you killed. Generally a heavy infantry man was trained to hold off the enemy with their large shield, sometimes using it to bash and off balance an opponent. But then wait to deliver quick stabs at the abdomen when the opportunity arose. Again it's nothing like in the movies. You stay in formation or you get killed.

Hope this helps get you started