Who runs the show, & what is their command structure like?
Here’s the top guy: Abu Bakr al-Baghdadi - Wikipedia
In terms of command and control for foreign attacks, ISIL is more distributed than Al Qaida. While AQ organized itself into cells, one could generally follow some type of line of control, often up to AQ’s central shura, or council. That’s why a guy like Khalid Sheik Monhammed had such an active hand in many plots, while being very senior.
ISIL tends to take a different approach to terrorism. The idea is more like inspire random people to do stuff, and someone will listen. As far as battlefield command, ISIL reportedly includes a number of former Iraqi army generals, likely indicating a clearer role for leadership.