Given that the root of the discussion is about Internet Archive being hit with huge traffic and not the functionalities provided by Wayback Machine, it very much is a distinction with a difference.
So Internet Archive, Archive.today, Archive.ph, etc. are all just means to the same end.
The internet archive is not designed to circumvent anything. It is not designed to "grant access without having your own access".
Archive.org exists to preserve historical snapshots of the public parts of websites, and not to bypass subscriptions or pay walls.