Erm -
no, they aren't. The domain in that scenario is
domain.co.uk.
Among other things, I am a hosting and registration provider. You don't have to separately register the www variant, it's just a question of adding A records.
The unqualified domain and the www variant are, in essence, machine addresses, i.e.
hostnames. They are two A records on the same domain.
Your policy would be a little clearer if your terminology were correct. Don't misunderstand me- I understand your policy; the blank and www variant of domains are conventional usage, but there's nothing magic about them= you can set up an arbitrary number of A records for a domain. If there were a single licence level for a domain, it wouldn't be possible to have an API key that included a "domain" check.
But please be clear- you're not licensing at domain level at all, you're licensing at hostname level, and your "multi-domain" licence should be a "multi-host" licence.