Champions are the cards that you play in the Champion Zone that attack your opponent and activate effects. Some champions have effects, others don't have effects, and some mix together!
Tricks are the cards that can be played as many times as you want. They are played from your hand and depending on the card, goes to the GY (Graveyard) or goes to your Trick Zone.
Arenas are cards that effect the entire field. Whether its boosting stats, drawing extra cards, or activating special effects, they can either be helpful, or unhelpful.