Enduring, as an adjective, means lasting for a very long time — a friendship, a story, a peace, a piece of music that people still love many years later. It has a quiet, serious feel. You would not use it for a headache that lasted all afternoon; you use it for things that stay. Though actually, the same spelling can be a verb form: "she is enduring the pain" means she is going through it now. When enduring sits in front of a noun ("enduring fame"), it almost always means "lasting."