They may or may not be interchangeable. Don't you love languages? example of an interchangeable situation Home alone: Home by himself Examples where alone can't be replace with by ...self. Oh my God, I felt so alone (lonely). That's not enough burgers; the kids alone will eat that, never mind the adults (just the kids without the adults will eat all that and then there will be nothing left). I alone know the secret of the tomb (only I). And there will be others. If they are interchangeable I would use either, or even "on their own".

Thank you for the help, Akayla! If you are interested in practicing your Portuguese, feel free to contact me, it would be great! I need to practice my English.

I was alone, by myself, on my own. Alone, I went to the house = I went to the house by myself. Alone is interchangeable with 'on my own/ by myself' or 'lonely'. It's easier to know the difference because lonely is a feeling and 'on my own' a statement.