Safe Mode will HOPEFULLY allow you to get into the OS, this is the only answer that allows you to access the INSTALLED OS. Booting from a live CD/USB will load an OS that will likely work, but it will not be the one that is installed. There is no such thing as DEFRAG mode booting, and DEFRAG is used to optimize a file system/storage device. The OS is found but it is running into problems as it loads - checking boot priorities will not solve this.
Safe mode is a diagnostic mode of a computer operating system (OS). It can also refer to a mode of operation by application software. Safe mode is intended to help fix most, if not all, problems within an operating system. It is also widely used for removing rogue security software.