To me, there is loneliness and aloneness.
Loneliness is needing to be around others because we are social by nature.
Aloneness is the fact that we are alone, that we are separate from all others, even those who we choose to be with when we are feeling lonely.
I struggle with both, but I know I could do something about the loneliness. Whereas the aloneness just is, and it is something I struggle to accept and something I sometimes rejoice about
: I am me, I have my own thoughts, my own mind, my own wishes.