Each country has its own set of domains, ICANN administers the main .com and .org domains, while in the UK Nominet does the .uk variants. Although I suspect that some of the much smaller countries use a shared regional administrator.
Yes, there are more places than the US, more administrators than just ICANN, and more TLDs than just .com and .org
So the whois tool should first check the type of TLD and then go to the authorising country's administrator and search that database. I've just searched for a .com that a client owns, and it tells me that it is registered via tucowsdomains.com and quotes ICANN, although it was bought from a uk registrar (and it tells me that as well). But when I search for the same client's .co.uk domain, it gets it from Nominet, and the domain was bought via the same uk registrar.
Finally, this might help you - https://en.wikipedia.org/wiki/WHOIS