You can boot into fastboot (a barebones flashing and unlocking mode implemented by the bootloader itself) and recovery (a real kernel + minimal UI on top to apply updates and wipe). From fastboot mode, you can boot into an arbitrary image, but that obviously requires an unlocked bootloader. Unlocking the bootloader almost always performs a wipe "to protect data".

In principle, it should be possible to have a diagnostic mode the same way recovery is implemented. But there are no device I know of that have this.