The difference for me is that I experience social anxiety differently than I experience being inherently a socially square peg in a round hole. A large part of my social experience is that people expect me to be a different person than I am and behave in a different way than I feel comfortable. That’s a very different feeling from how I experience social anxiety or otherwise feel shy. It’s essentially a performance, often called masking, and I have a different (quite a bit less usually) capacity for it than I do all of the challenges of being socially engaged when I’d rather not for my own space.

One is enjoys your own company and the other is an excuse because you’re too anxious to socialize but would like to and feel lonely otherwise.

This is exactly it. If you drugged me, put me on a plane, and made me parachute into a random social situation while still groggy, I'd do great. I just feel no particular inclination to socialize. I recognize it's not great for personal and professional development, so I push through the indifference anyway, but my idea of a good time is wandering through some quiet old place with a camera.