Barriers are used in Hazardous locations to power Intrinsic Safe instruments. The barrier will reduce the available loop current to a level that cannot produce a spark.
An Isolator is used to connect signals of different common mode voltage for example a transmitter signal may be referenced to +24 whereas the DCS may be referenced to ground.
You can also have an isolator that is designed for use in Intrinsic Safe circuit.
A barrier is a Passive device but Isolator is an active device and needs power.