They are different operating systems.
Linux is able to read MS Windows filessystems (msdos, vfat, ntfs) by using the appropriate filesystem modules that are usually installed by default. Reading Linux-specific filesystems on Windows requires special software.
Linux is able to execute MS Windows binary executable applications by means of emulation (wine is the tool for this) - this seems to work for many applications, though not for all. You can run Windows as a virtual system in Linux. Windows doesn't care about Linux executables, but you can run them either compiling from source code on Windows or by installing Linux in a virtual system (like VMware or VMplayer or VirtualBox or Quemu).
Several applications are available for both Linux, Windows, BSD and Macintosh systems (one such example is OpenOffice).
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T74marcell
Arch Linux