I don\'t want to know if there is a one-to-one equivalence between API functions in windows and linux, neither want to know every API function.
I just want to know t
If you want to port an application that uses Win32 calls, your best bet might be to use WineLib. This uses the libraries underpinning Wine, but it's not the same as just running an application using Wine -- you re-compile your application as a Linux application, just using the WineLib shared libraries. It will still look like a Windows application though, unless you then modify the UI layer.
As has been said elsewhere in the answers, there's no real direct equivalent to Win32 in Linux -- different bits of Win32 are provided by different components, and sometimes you've got a choice of components. This is possible because some equivalents of parts of Win32 are implemented natively at a lower level -- for example, Win32 provides UI components, equivalents to which are available in either GTK, Qt or any number of other toolkits (like WineLib), which themselves interact with X. Just as you would usually use components from Win32 rather than drawing your own using lower-level API calls, so you'd normally use components from your high-level UI toolkit rather than using X directly.