Stdout and stderr are directed to the terminal by default. Stdin is directed from the terminal by default. They can be redirected (elsewhere) with
Also, when you type textual (displayable) characters (on your keyboard),
they are (usually) echoed to the terminal. (So a command is not the only source of terminal output.)
A note on copying
Does it mean that it is copied? No: this does not imply copying, but don't take this sentence to imply that it is not copied. Just know that it gets there. At some point the character codes are converted into pixels for display; up to then there may or may not be copying (copying is just an implementation detail).
Answer to revised question
Yes: stdout and stderr are streams (like a river, once part of the river has passed, it does not flow back. But unlike a river, you can make a copy as it passes.)
You can re-direct to somewhere else. If you want them to go to two places, then you can copy/duplicate them.
tee is a good tool for this. E.g.
ls | tee some-file will copy to some-file and write to stdout. Note some-file can be any file, e.g.
/dev/stderr (if it exists on your system).