Why and how does Magento differentiate between setup, read, and write database resources?

This is because Magento supports master/slave configurations for databases.
You can set a master database that will be used for writing (and setup maybe) and a slave database to read data from.
If you want to try it, here are some references explaining how to do it:

• https://www.sonassi.com/knowledge-base/magento-kb/magento-mysql-optimisation/ this one is very complex and has a lot of details.
• http://magentocommerceblog.blogspot.ro/2012/04/how-to-setup-mysql-master-slave.html short and to the point
• https://stackoverflow.com/questions/10881213/magento-mysql-master-slave-replication-slave-not-used same as the one above. I've added here in case you are a fan of SO. :)