There are four modes altogether and they are:
Story Mode
Play the Story mode to earn Stars, Gems, Eco-Sphere, and Runes. Use Story mode as a training ground for testing out new teams and for leveling up new Ghosts.
Daily Haunt
The Daily Haunt is similar to Story mode in that you will be fighting AI. The Daily Haunt is where you farm your Elemental Shards with each day a different type of Elemental Shard becoming available as a reward for clearing the stage. At the Weekends the Daily Haunt will offer random rewards.
Gozer's Tower
There are 50 floors in Gozer's Tower and you have to battle your way up floor by floor defeating the waves of enemies to earn rewards that get increasingly better as you reach higher floors.
Ghost Arena
This is a PvP arena where you battle against other players' Ghost team. As you progress through the leagues, the coins and PKE Crystals you get for winning a battle increases. As your rank increases, you become eligible for more lucrative prizes at the end of each season.