Well, arxiv-vanity.com uses a different TLD than arxiv.org, and their respective url schemes are completely different. arxiv-vanity.org is hosting a redirection site that interprets the arxiv.org path scheme and redirects you to the correct arxiv-vanity.com url.

I originally bought the arxiv-vanity.org domain and set it up as some rewrite rules on my personal caddy server. The owner of arxiv-vanity.com thought it was cool so we got everything transferred over to them now.