You have to realize that Windows runs Windows softwares and Linux runs Linux softwares...
I have never tried Parallels Desktop, but I believe it works like virtualbox, vmware, and qemu to some extent etc. And differently from wine.
In wine, you do not need to install MS Windows it tries to have linux understand what the windows program wants.
Parallels, Virtualbox, vmware, and qemu emulate a machine, a PC for example, on which you can install a different OS. The trick is that both OSes run at the same time on the same machine. Plus, if you have virtualization (Parallels, Virtualbox, vmware, Qemu+kqemu/kvm) the guest OS can use the real hardware and not an emulated one, and runs faster.
In this case, Windows softwares run in Windows, and Windows runs in Linux. (Whereas with Wine, Windows apps run in Linux, which is a bit incestuous and so it does not always work.)
The trick you see often is to maximize the window containing the guest OS and have Windows XP not display the desktop, this way, it feels like both OSes merge. It is only a visual trick: you cannot see it but it is there. And another trick is to use rdesktop to start guest-OS apps from within host-OS.
Windows apps will never run natively on Linux.
Now if you would say what Windows apps you want, there are possibly linux alternatives. If you are into games, you can try cedega.
Have a look at wikipedia on virtualization, etc.