ISIS in Libya is pretty far afield of ISIS in Iraq and Syria. Far from the fearsome caliphate spanning two borders, the Libya faction got its start as an Islamist group with a single small town along the Mediterranean coast.
Since pledging allegiance to ISIS in October, the group has grown significantly, and has attracted some recruits. They’ve got a presence in several towns along the coast now, but they’re no caliphate.
The name has a lot more significance than the Libya wing itself, however, and those few possessions in the Mediterranean have European nations, particularly Italy, panicking over the prospect of “an ISIS invasion.”
Libyan ISIS is in no rush to correct them, and seems to be delighting in punching well above its weight, even if in practice they’re very much a second-tier power in Libya, and certainly no threat to conquer Rome. The reputation boost, as with the ISIS parent group, is everything, and may ultimately make them far larger and more dangerous than they are now.