When someone is alone it means they have no other people with them at the time. When someone is lonely, it means they are craving for someone else's company. Someone can be alone and not lonely, and someone can be in a crowd of people but still feel lonely.

Check answer here: http://dictionary.cambridge.org/grammar/british-grammar/alone-lonely-or-lonesome

There is no difference in my eyes Whether physical or psychological lonely lonely no difference in nature That's all

Lonely is a feeling that you are lacking companionship whereas 'alone' can simply mean that you are by yourself. Saying that you 'feel alone' can mean that you feel lonely or it can mean that you aware of the absence of other people, more of a creepy feeling. It depends on the context. Espero que no te haya confundido aún más.

I remember so lonely is adverb alone is adjective