You can call or put in American, Bermudan, or European exercise style.
But they become activated (or extinguished) only if the underlying breaches a predetermined level (the barrier).
"In" options only become active in the event that a predetermined knock-in barrier price is breached: "Out" options start their lives active and become null and void in the event that a certain knock-out barrier price is breached: Some variants of "Out" options compensate the owner for the knock-out by paying a cash fraction of the premium at the time of the breach.
While it seems straightforward to define a barrier event as "underlying trades at or above a given level," in reality it's not so simple.
Barrier options can have either American, Bermudan or European exercise style.