Take it up with Wikipedia. like someone else pointed out there is not really a consensus as to what is specifically called a continent or even how many continents there are.
https://en.wikipedia.org/wiki/Continent
Oh look Australia has 2 pages, one for the country:
https://en.wikipedia.org/wiki/Australia
and one for the continent:
https://en.wikipedia.org/wiki/Australia_(continent)
Should you find it weird when any Australian calls themselves Australian and not Commonwealth of Australian? Because as you can see that's the full name.
I'm from Colombia and thought it was weird at first since in Spanish you refer to Americans as Estado Unidenses. Which in hindsight is the weird thing because you don't really do that for other countries. You don't call people from la Republica de Colombia "Republicanos" you call them "Colombianos".
If people from the United States of America want to call themselves Americans, then it makes 100% sense since the "America" in the name of the country is the only part that's actually a proper name and not a descriptor.
Linking here the demonym from people for the United States of America is Americans because United Statetians? would just be weird.
https://en.wikipedia.org/wiki/Demonyms_for_the_United_States