No difference. Uttaranchal was the official name from statehood (Nov 9, 2000) until Jan 1, 2007, when the Uttaranchal (Alteration of Name) Act, 2006 took effect, renaming it Uttarakhand.
"Uttarakhand" (उत्तराखण्ड) means "Northern Land" in Sanskrit—the traditional name for the Himalayan region in Hindu texts (Kedarkhand, Manaskhand). "Uttaranchal" was a colonial-era administrative coinage. The BJP-led state government, backed by cultural groups, pushed the restoration. Parliament passed the bill Dec 2006; President assented Dec 21, 2006.
Older documents, exams, and habits still use "Uttaranchal." Both refer to the same state. No legal or administrative distinction exists.