Messing with several versions of drush
You are mixing up the globally installed Drush with a locally installed Drush. To run the local Drush from your project, run vendor/drush/drush/drush --version from inside your project. This will give you 8.0.0 which is a bit old. Better get the latest Drush 8 release with composer require drush/drush:^8. Currently this is Drush 8.4.8.
Next, you can consider to either update the globally installed Drush (not recommended) composer global require drush/drush:^8 or alternatively (recommended) install the Drush Launcher instead. The Drush Launcher is just a wrapper command to always pick up the project-local Drush. So you can easily run Composer-based D7 and D8/D8+ projects on the same machine in parallel and calling drush --version in a project will adjust accordingly.
If your project is D8 or D9 install Drush 10 instead composer require drush/drush.