Patrickv again hit the nail on the head. Those are the exact two applications I use for my network FTP's. Bulletproof FTP for the server side application and FlashFXP for the client side application. Both, in my experience of running mutiple FTP's, are extremely well equiped and very efficient / easy to use in my opinion. I too definitely recommend both of those applications.
As for the file sharing software without the use of FTP's I'm not entirely sure on if there is an alternative to the Windows File Sharing Feature. Although if there is I'm sure someone will have a decent suggestion in mind

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Breaks.