What is Composer ?
Composer is a tool for dependency management in PHP which requires PHP 5.3.2+ to run. Composer can be very usefull specially when youre module needs other dependency module or library.
Sometimes when the module is dependent to other modules and you manual install in Drupal admin page ,Your module cannot be installed right away because it requires another module for example. "Phpmailer".
A developer might be having a hard time to figure it out and also waste of time just to install a single module when we don't use composer.
Composer is very handy to use and takes only 1 line of script . Ex. composer require drupal/phpmailer
Composer is a cross platform and make it run equally with macOS ,Windows and Linux .
What is Drush ?
Drush(Drupal shell) is a command line tool intended for Drupal CMS site building. Most pronounce Drush so that it rhymes with hush, rush, flush. See more details on Top 5 Useful commands from Drush
Once you already install the module , it is not yet usable because you need to enable it via Drupal Admin Page GUI or via Drush command
Ex. drush en phpmailer