First, note the IP addresses for the two Macs. On the Mac OS 9 Mac, open the TCP/IP control panel and the IP address should be shown in that window. On the Mac OS X 10.4 Mac, it is in System Preferences under the TCP/IP tab (or use the System Profiler app).
File sharing from Mac OS 9 to Mac OS X 10.4 is definitely possible. Make sure File Sharing is turned ON on the Mac OS X 10.4 side; you do that in System Preferences Sharing pane. FIle sharing does not need to be turned on in Mac OS 9. On the Mac OS 9 side, go to the Apple menu and select Network Browser. See if the Mac OS X 10.4 Mac is visible in the list. If so, select it and go through the login window by giving user name and password and then selecting the volume or user folder to mount. If it is not visible through browsing, you should be able to connect by using the IP address. Click on the little button with an icon that looks like half a globe on top of a hard disk. Select Connect to Server... Enter the IP address for the Mac OS X 10.4 Mac and click Connect.
File sharing from Mac OS X 10.4 to Mac OS 9 will probably NOT work. Mac OS X 10.3 was able to do it, but Apple removed "AppleShare over AppleTalk" starting with 10.4. There is a product that adds TCI/IP file sharing (no need for AppleTalk) to Mac OS 9.
http://www.opendoor.com/shareway/
I have this installed on a Mac OS 9 Mac. I can use the Finder's menu -> Go -> Connect to Server... window. Click Browse. The Mac OS 9 Mac shows up on the browse list. If it did not show on the list for some reason, I can enter the Mac OS 9 Mac's IP address on the Connect to Server window and click Connect.
FileMaker Pro version 6 was the last version to run on Mac OS 9. The CD (at least the one I had) also had the Mac OS X version on it, although I'm not sure if it is compatible with later Mac OS X releases. It was definitely compatible with 10.3.