Having multiple Drush instances for different core versions
Ideal way would be to use Composer to set up your projects. I'd recommend Composer templates for Drupal projects. Then add Drush to your project: composer require drush/drush.
Now install Drush Launcher on your machine, globally. Drush Launcher provides a drush command that always finds and uses the locally installed Drush from the /vendor folder.
$ cd MYDRUPAL
$ drush --version
Drush Launcher Version: 0.6.0
Drush Commandline Tool 9.3.0


But probably you can not simply rebuild your projects. Then you may want to install two different global Drush versions. See https://github.com/drush-ops/drush/releases for all available versions.
drush8
$ sudo git clone https://github.com/drush-ops/drush.git /usr/local/src/drush8

$ cd /usr/local/src/drush8

# Check the latest Drush 8 version at https://github.com/drush-ops/drush/releases
$ sudo git checkout 8.4.6

# Linux:
$ sudo ln -s /usr/local/src/drush8/drush /usr/bin/drush8

# Mac:
$ sudo ln -s /usr/local/src/drush8/drush /usr/local/bin/drush8

$ sudo composer install

$ drush8 --version
Drush Version   :  8.4.6

drush9
$ sudo git clone https://github.com/drush-ops/drush.git /usr/local/src/drush9

$ cd /usr/local/src/drush9

# Check the latest Drush 9 version at https://github.com/drush-ops/drush/releases
$ sudo git checkout 9.3.0

# Linux:
$ sudo ln -s /usr/local/src/drush9/drush /usr/bin/drush9

# Mac:
$ sudo ln -s /usr/local/src/drush9/drush /usr/local/bin/drush9

$ sudo composer install

$ drush9 --version
Drush Version   :  9.3.0

Source: Installing &amp; Using Drupal Drush on Debian 7 (Bookmark this!)