Alone but not lonely

I like doing stuff alone, like going out to buy groceries, going to the library or a coffee shop, eating, walking back home, or riding a bus. The reason I do this is because it is liberating, it sets my mind free, gives me time to think, contemplate, wonder, imagine, evaluate, obsess. However it does not mean that I don't want people around me, that I am not social, that I am lonely.

I enjoy being alone but then there  are times when I see people around me, people having fun with their parents, lovers or friends and then I miss my loved one's and suddenly I realize being alone and lonely are two different things, and  I don't want to be lonely.

I have always heard people say that they are alone but not lonely, but frankly I never really understood the difference but yesterday I had gone out to the market with a friend, now usually I go out alone and I do enjoy those walks but it was pretty fun with a friend as well and it was then that I realized that the difference between being alone and lonely is that when you are alone you do have the choice not to be when you want to, you can just be around people and feel normal, but feeling lonely is when you are around people yet you feel alone. Being alone is a physical phenomena and being  lonely a mental one, it is when you feel alone. So now I can say with surety I want to be alone but not lonely