- archive.org is the older of the two. It has 29 questions at the moment, and it also has a tag-excerpt and a tag-wiki. The tag excerpt says: "The Internet Archive and the Wayback Machine."
- The tag wayback-machine only has two questions, one of them has both of these tags. (I have posted those two questions in this site's chatroom - so they can be found there even if the tag gets removed.)
- wayback-machine was also created (and then removed) back in 2014: https://webapps.stackexchange.com/posts/69847/revisions (Some relevant SEDE queries: adding this tag, removing this tag, deleted posts with this tag.)
Of course, the tag with only two questions could easily be manually retagged. But I consider the synonym suitable. Both names for this site are commonly used, so people trying to add suitable tags to their question are likely to try either of them. Moreover, with the tag synonym in place, it is no longer possible for the tag to be created and removed again.