I would define being alone as simply being on your own whereas being lonely is temporarily by yourself. The significance in that difference is that being lonely should be embraced and welcomed.
We should all be able to adapt to an environment and learn to feel settled within ourselves. A momentary feeling of loneliness is to be appreciated when considering what it feels to be alone. The latter has the capacity to impress upon our outlook of the world and the thoughts we formulate. We manage loneliness versus survive being alone.