Wayback Machine alternative
When a public archive is not the record you need
One archives the web on its own schedule and lets everyone read it. The other captures the URLs you name, when you say, into a file you own. Most people searching for this want the first one.
Stay where you are if
You want the public past of pages nobody captured on purpose, or a citable public URL for something already online. A capture starts existing when it is requested, so nothing here reaches back before today.
Move here if
The record has to exist on your schedule, in a format you chose, inside storage you control — and be produced by a request your code can repeat and your auditor can read.
What moving looks like: There is nothing to migrate, because nothing you have is in an export: point requests at the URLs that matter, write the artifacts to your own bucket, and re-issue on the schedule the record needs.