Entirely means in all parts. You just pointed out that they both involve control of publishing. So let me rephrase. The first laws to restrict copying were aimed at censorship.
Remember "The government" doesn't not exist as a discrete rational and acting entity. It's an abstraction and obscures that is really going on. A good number of people with strong influences on those who act officially and unofficially as "the government" do have a great deal to gain from copyright. Or do you claim it is simply a coincidence that copyright terms always increase to include mickey mouse? Those with influence in the status quo love gather whatever sort of mini-monopolies they can to assure their continued influence.
Common-law provided control over the physical manuscript. If I then let you read it upon your representation that you won't publish it without my permission, then you are estopped from publishing without permission. Moving control from my copy to all copies owned by anyone is a large jump. People have controlled their own stuff for thousands of years, but not the expressions that may be fixed therein.
I didn't say they are they same in all or even most essential qualities. I just said that there are some number of qualities sufficient to define a category containing both concepts, but still excluding of the great majority of concepts. If you want to reject my statement, you should poke at one of the six implied premises of it.