[Jonathan Capra]"But in Motion do I just have to save different copies of the project and render each separately?"
How is that really different from what you do in FCP or AE?
FCP allows you to have many sequences in one project file. AE allows you to have many compositions in one project file.
Motion, for better or worse, is a single composition per project, but you can duplicate your project files in the finder & modify them, or you can modify them and then use "Save As" to create variations. Either way, you're doing the same thing that you would do with duplicate timelines or compositions in FCP or AE.
[Jonathan Capra]"I have a Motion project that moves a bunch of Drop Zones around in a motion. I want to output 4 or 5 different versions of this animation with different video in the drop zones."
If you are using Drop Zones, you create the first version by inserting your clips in the drop zone, then output to a self-contained movie. Replace the clips in the drop zone with your version 2 clips, output to self contained movie. Repeat for each version.
With Motion's drop zones, you can create a single Motion project and simply replace the clips to get different finished version. The thing to remember is that once you change out the clips, you have lost that version.