In bash, calling foo would display any output from that command on the stdout.
foo
Calling foo > output would redirect any output from that
foo > output
Something to add ...
The package unbuffer has support issues with some packages under fedora and redhat unix releases.
Setting aside the troubles
Following worked for me
bash myscript.sh 2>&1 | tee output.log
Thank you ScDF & matthew your inputs saved me lot of time..