the dot at the end is an ambiguity in a few specs. if I recall correctly, dns requires to end in a dot as it signals the root servers or something, but obviously can be left empty.
then browsers started to support it, but over time bugs pilled up and now it is treated as a different hostname (e.g. "www.example.org" is completely different to your browser than "www.example.org." even though they are the same to the dns spec)
then tls specs considers the dot in an earlier version, and they should be the same but because of the browser bugs it is all too much fun. my bank actually has a server that replies the same for domains with or without the root dot. but they only signed their certs for the no dot name, which again, is the same, but for browsers is kinda of not.
The dot at the end has a technical meaning in two different contexts. The first is to disable search lists in the DNS stub resolver. If you try to look up, say 'ai', then the sub resolver is likely to append your current domain name during the lookup. Looking up 'ai.' disables that.
The other use is in DNS zone files where everything that does not end in a '.' get the name of the zone appended.
The for mail (SMTP) the dot at the end is implicitly present, and adding one is not allowed.
HTML/HTTP basically doesn't define semantics with respect to the dot at the end. That's why "www.example.org" and "www.example.org." are different. They are different strings, and nobody defined them to be equivalent. At the same time, the name is just passed to the stub resolver in many cases. So search lists may be applied under the hood.
That's one of many ICANN rules which don't apply to country-code TLD operators.
Another example of a rule that's optional for them is ICANN's Uniform Dispute Resolution Policy. Indeed, only some of them have adopted it, with others using a variation and still others not basing any of their dispute mechanisms on the UDRP.
(Also notable, they have an A record on the hostname "ai." - you can see their website at http://ai./)