No, they aren't the same. AVI is a kind of a rough audio/video file format that conforms to certain specs. But you could still have AVI files that were encoded differently. Xvid is a compression codec, a specific algorithm to compress audio/video data. For example, you could have an AVI file that was compressed with Xvid, or an AVI file that was compressed with Divx, or an AVI file that wasn't compressed at all. As long as they all conform to the AVI file structure, then they are all AVI files. The compression of the video is one thing, the file format of the video is another thing.
Ok heres my problem I have a file that I want to put on a disc that is xvid. So do I convert to avi than convert with avi2dvd? Or what do you guys suggest?
If you have an XviD video file you'd want to encocde it to DVD compliant mpeg2 then run it through an authoring program to write the DVD files. Also, there are lots of 1-click software programs like NeroVision Express where you could just load your XviD file and it will re-encode it, author it and burn the DVD.
I mostly use MainConcept to encode to mpeg2 and then TMPGEnc DVD Author to write the DVD files. I don't know about freeware mpeg encoders. I think DVD Santa should be able to encode your XviD to a DVD compliant mpeg. I haven't used it but it does have a free trial: http://www.dvdsanta.com/