The difference between a MAGE_RUN_TYPE website and store in Magento

So the other day I spent almost a day wrapping my head around a problem I ran into when I was trying to deploy a multistore- Magento site. The problem was that whatever I tried, the site kept showing the default Magento 404-page (not the sites’ one). I tried everything: Flushing all caches (local, memcache, read further ...