Factory images are bootloader compatible images, that is to say, they can be flashed using fastboot or alternative low-level tools or environment.
Full OTA images are over-the-air updates that are to be flashed via recovery environment. OTA updates are usually either incremental or full. Incremental updates require the user to be running a specific Android build (not just Android version) as they increment in the existing
build only. On the other hand, full OTA updates don't require a specific existing build to continue. They are handy when a user hasn't updated their system for a long time and wants to skip successive incremental updates.