There are two types of USB flash drives.
Zip drive emulators, and hard drive emulators.
I think you will find Tinycore can be installed on any usb drive with any option.
The zip option was included for those who have a computer with a bios which will not boot using the other methods. There are a few older computers, where this may be the case, probably around 10 to 15 years old.
A zip drive was like a floppy drive, but larger capacity. Some zip floppy disks were 100 mb. Some were 250 mb. Some people used zip drives before cd writers became common. Ordinary floppy disks were 1.44 mb (there were also others).
Very few people will need to use the zip option.
Very few computers will boot from a usb zip drive, but not a regular usb drive. There are some. Zip drives were common before usb drives.
If your computer works with another option, you don't need the zip option.