Under modern First Amendment doctrine, "freedom of speech" encompasses two different legal protections: first, that the government impose prior restraints (pre-screening what speakers will say), nor may it engage in retaliation (punishing speakers for what they've said).
At the founding, it was different. "Freedom of speech" encompassed the ban on prior restraints, but it did not provide anti-retaliation protections -- at least not as we understand them now.
So regardless of what you might be planning to say, the government was generally not able to pre-screen your words before you transmitted them to others. It couldn't demand to see what's coming off your press before it hits the streets, nor could it require you to obtain a license to operate a printing press if the outcome of that process involved a review of what you might publish.
Once you spoke, though, you were "responsible for the abuse of that freedom," meaning that you could be held liable for any harm that resulted; defamation, sedition, incitement, and the like were commonly understood at the time to be "abuses" of freedom of the speech.
Maine made this distinction explicit, where the U.S. Constitution did not, but both operated on this premise. For a very full explanation of this prinicple, including some mind-blowing examples of what the government considered an "abuse" of the right of free speech in the early days of the nation, see Eugene Levy's Emergence of a Free Press.
