Islanding operation is when disconnected from the integrated grid system and the powerhouse is supplying a local feeder only? I think isolated operation and islanding operation are different.
You define Island OK. Isolated Operation is Local power house, no feed from grid ever. Standard use of term "Isolation", when manually disconnecting to take from service or make safe, confuses meaning!!! Reading "Isolate" in normal English dictionary, not electrical may help.
For the 2nd line in your Statement - Power is supplied in ISOLATED OPERATION refers to POWER CONSUMPTION by the LOAD with in the CAMPUS of POWER GENERATION, NO POWER FLOW to the GRID.
ISLAND MODE MEANS the POWER FLOW IS THERE THROUGH THE GRID in addition to Power supply with in campus, but RESTRICTED TO SELECT AREA by the GRID CONTROLLING AUTHORITY and POWER GENERATOR HAS NO SAY in the DISRIBUTION OF POWER.