Lonely or alone?

As I sit here on my own, well, not entirely on my own, I have a snoozing kitty by my side, I have begun thinking about the difference between being lonely and being alone.
I'm sure greater minds than mine have addressed this question over the years and have no doubt come up with great philosophical treatises on the subject and that's fine, but you are now about to be regaled with my simplistic waffle on how I see the difference.
I have felt very lonely at times in quite large gatherings. Particularly where I've felt somehow out of place, Thanksgiving at my ex parents-in-law for instance as a foreigner celebrating the survival of people who left my country and whose descendants rebelled against her. That sounds a bit harsh and isn't exactly what I'm trying to get across. What I mean is that I felt alien, odd and somehow not needed. They didn't go out of their way to make me feel that way, in fact just the opposite but there I had an underlying feeling that they were somehow better than me because they had moved on. I don't know, I'm making a bad job of explaining.
A better example of loneliness perhaps is a more recent occurrence; I was on a train to Edinburgh surrounded by a group of women who had all known each other for a long time and were off to celebrate the 50th birthday of one of their number. One of these women said, very loudly as they were all quite 'happy' "we are all in relationships, we should have a get-together somewhere with all our partners....". At that point I tuned her out somewhat as the realisation hit me that I was on my own in life without a partner. To me, that was loneliness right there.
At other times I sit in the house or maybe in a pub whilst I'm away travelling, my trip to Las Vegas being a good example and think to myself that although I'm alone, I'm not lonely. I am enjoying my solitude and the peace it brings. It doesn't have to be a quiet place, I can be alone and content in the loudest of bars, I just sit in my little world and enjoy my introspection, watching the world go by.
I think loneliness comes when perhaps one expects to be in company and it turns out that although the people are there they are more interested in each other than in you or, as I said earlier you have little or nothing in common with those you are amongst.
I am not explaining myself very well but there is a big difference between being alone and being lonely. I'm just not very good at putting across what that difference is. I suppose we all react differently to our particular circumstances and what makes some people feel lonely frees others to be content in their solitude.
Still, I hope that people can learn to enjoy being alone as well as being in company and get the best out of all situations. One of the worst feelings in the world is feeling alone in a crowd and I hope that if I come across someone looking lost and alone I can help them to be free from the sadness that can bring and be clever enough to tell the difference between someone feeling lonely in a crowd and someone enjoying their solitude.
Anyway enough of this rambling, I may well try to revisit this subject another time and hope that I can convey my thoughts a little more clearly.
Until then, Peace and Love ttfn x