One of my favorite things to tell my best friends is, "You may feel lonely, but you're never alone." I see the distinction between them and I want to emphasize that however shitty they may be feeling, there will always be someone there for them.
When it comes to me, however, I can't tell the difference. I have a tendency to withdraw when I'm feeling blue, so in my loneliness, I automatically assume that I am alone, even though there are quite a few people willing to reassure me if only I had reached out.
It's one of the lessons I'm still learning, and I'm having a hard time with it, too. But with any luck and a lot of patience, maybe this is an area of myself I can improve on.