Typically, "loneliness" is what we call sadness within the experience of being alone (although I think sometimes it is other parts of the experience, too). Being alone is an entire mode of funcitoning, which contains the full emotional spectrum - joys as well as sorrows.

Being alone also has its own type of cognition: specific perceptions, possibilities and impossibilities, etc.

It's my observation that being alone can produce serious cognitive errors, most particularly when it is confused; i.e. partially embraced, partially rejected, not recognized for what it is, etc.

What seems possible "with other people" while one is alone is importantly different from what is actually possible in a group.

We need to question the solitary feelings of omnipotence that we are encouraged to embrace (confidence, etc), and learn a new kind of power.