Core
Cores are alternate styles that you can pick by holding up or down on the Style Select screen. Generally speaking, which core you choose determines the pace of gameplay.
Nightcore
Nightcore is the fastest core available. It decreases Hitstop and increases Air Control. It can be selecting by holding upward on the style select.
Breakcore
Breakcore is the default core. It still has some Air Control and a moderate amount of Hitstop, but it's mostly a middle ground between Nightcore and Daycore.
Daycore
Daycore is the slowest core, but it will also be the most familiar to players of regular fighting games. It completely lacks Air Control and has the most Hitstop of any core.
Secret Cores
In addition, there are also some secret cores with their own methods for being selected. Those won't be spoken much of here.