z@host:~$ cat bash_script ; echo
#!/bin/bash

echo "Error: something went wrong" >&2 #print to STDERR
echo "Status: running" #print to STDOUT

z@host:~$ ./bash_script ; echo
Error: something went wrong
Status: running

z@host:~$ ./bash_script 2> error_log ; echo
Status: running

z@host:~$ cat ./error_log ; echo
Error: something went wrong

z@host:~$