Why there are 2 directories having same content?
/proc is a "virtual" filesystem exposing some kernel and process related details.
$$ is a shell variable giving the PID of the shell running it.
/proc/$$/root is a symbolic link to the root directory as seen by the current shell.
This could change in case you are chrooting.
In short, the two look identical because they are the same directory. If you execute ls -ld /proc/$$/root you will see that it is a symbolic link to /, and therefore /proc/$$/root/bin and /bin are the same directory.