Factory images are for flashing routers with OpenWrt for the first time using the web interface of the original firmware.
Sysupgrade images are for flashing routers that already run OpenWrt. The image can be applied using the web interface or the console.
Linux kernel as a separate image.
Root file system as a separate image.
Image that is meant to be flashed on an SD-Card.
Image that can be applied using the TFTP meachnism of the bootloader
Image of unknown purpose.