@abc.xyz is arguably even easier to communicate than @gmail.com or @yahoo.com because it's possible some people may have never heard of such and such popular mail host, but at least they know the alphabet :-)
Apart from that, it’s mostly what people browse to, yes. So .com, .net, .org.
If it's clear I'm not local, something like "yahoo.ca" or "mail.ru" is not confusing, except perhaps for Colombians (.co). A local with an address in the "wrong" country can be confusing if it's obscure.
Within a country, using a less-common second level domain (e.g. .org.uk) for a personal domain can be confusing. I've had people say "so that's example.org.uk.com then?" or "what was that, symbiote-example.org.uk@gmail?"