This is far to confusing to explain when you are using the same names.
It's like trying to understand Who's on first for the first time. Try using
different folder names until you can get it working then worry about what
things are called.
To try and help the only thing I can say is if the files have the same
exact names and you use the "with replacing" it will overwrite what ever is
in the destination folder. If you are saying the source folder is being
deleted then you are having an issue where the files are being moved and