Question

why a usb drive can work in both linux os and windows os without the need for formating the file system?

Answer 1

Typically USB drives are formatted with FAT32 or NTFS, both of which are usable in Linux.

You might also find the Wikipedia article on USB mass storage devices interesting. In particular:

The USB mass storage specification
does not require any particular file
system to be used on conforming
devices. Instead, it provides a simple
interface to read and write sectors of
data—much like the low-level interface
used to access any hard drive—using
the “SCSI transparent command set.”
Operating systems may treat the USB
drive like a hard drive, and can
format it with any file system they
like.