We are not alone.
We feel alone.
"I'm alone but I'm not lonely"
"I'm not lonely, although I happen to be alone"
We experience the feeling of being alone, and the emotion of being lonely.
Informal recording of mental activity: Some of these thoughts reoccur in different forms and eventually coalesce into more formal writings, and some are more catharsis than exposition. (A.K.A. Extra Gravy)