To be lonely is to be aware of an emptiness which it takes more than people to fill. It is to sense that something is missing which you cannot name.
Frederick Buechner, Whistling in the Dark
Being alone and being lonely are two very different things.
The worst kind of loneliness is what I think of as “Rudolphian” — as is Rudolph the Red-Nosed Reindeer. He isn’t accepted for who he is because he’s different. As such, they never let poor Rudolph join in any reindeer games. That’s the lonely-in-a-crowd loneliness. It’s very much a what’s-wrong-with-me loneliness.
At the same time, introverts recognize their own need for solitude. Being alone is a place to regroup and recharge. It’s a place to gather thoughts.
Thomas Merton said, “As soon as you are really alone, you are with God.”
Being lonely can come from being excluded, but being alone can lead to the place of recognizing how included we are in something far bigger than anything we can imagine.
Hot Dogs and Marmalade 
I learned the difference the hard way- but the good news is now I love my time alone. Prefer it in fact to time spent with others.
Good quote from Thomas Merton.