yhea pretty much.
there is maybe a slight difference in that alone is also a feeling or a state of mind e.g. feel alone, be lonely. This is why you will also hear things like "I never feel so alone as when I am in a crowd of strangers".
where as "on my own" or "by myself" don't have this feeling/hint of being lonely.
I would say both get used when speaking, if alone doesn't get used as much I would say it's because of it's secondary meaning.