DAPCHI, Nigeria—As evening prayers resounded across this northeastern Nigerian town last month, camouflage-clad jihadists drove up to a local girls’ school and kidnapped 110 students in a replay of one of the world’s most infamous abductions: Boko Haram’s 2014 seizure of 276 girls, hours away in Chibok.

But the Feb. 19 attack was different in an important and unsettling way, according to U.S. and Nigerian officials. The culprit wasn’t Boko Haram, but a breakaway faction that is allied with Islamic State and, in the eyes of...