as Irfan pointed out in his comment, "Image" means creating a partition image (using dd). Normally, TWRP creates tar archives with all the files located on a given partition, which then is much smaller.
"Data" contains all data – i.e. data & configuration from system apps as well as user apps. As the /system partition is mounted read-only during normal operation, that's where all "variable data" go (apart from files you store to the SD card).
Probably none of those. It's unlikely Odin understands any of the TWRP backups (you can try, and I stand corrected if you find out it can – but no guarantees from my side, including that it doesn't "brick" your device – I'm not a Samsung user)
Vendor is stuff very specific to your device provided by the "vendor", i.e. usually the manufacturer (including customizations) – while System is the "Android base" (though this separation is rarely absolute)
Same as between "System" and "System Image" (see 1.)
ddbackup i.e. the exact copy of whole partition (to retain Verified Boot), the other one is
tarbackup i.e. the contents of filesystem. I don't think restoring TWRP backup through odin would be possible but I never used Samsung device. May be the Images can be restored. All of the remaining questions are answered once you know what these partitions contain.