Well at least Adams described it appropriately. It’s just that sometime between then and now we started calling it “Independence Day”.
Nowadays it’s more often than not referred to as “the Fourth of July”... all meaning washed away. I think this has been slowly done deliberately, and (some) people just give in to it without thinking.
This article explains that “the Fourth of July” is was in use (scarcely) towards the end of the 18th century, HOWEVER I still think liberals make a concerted effort to suck the meaning out of it: