There is no science to testing, no provable best way, despite many people's vehement opinions

You forgot a hope-driven development and release process and other optimism based ("i'm sure it's fine" method), or faith based approaches to testing (ship and pray, ...). Customer driven invluntary beta testing also comes to mind and "let's see what happens" 0-day testing before deployment. We also do user-driven error discovery, frequently.