The meaning of free speech has changed dramatically over the past century. This is why things can seem so contradictory.
Like so much of Anglo-American law, Free Speech and Freedom of the Press is an application of the fundamental concept of Due Process of law. One facet of Due Process says that the government cannot single out individuals, groups, or specific types of behaviors unless there's a compelling reason and the targeting is necessary. All laws should be generally applicable and targeted to addressing identifiable harms, on the one hand, or achieving some broader policy objective on the other.
A.V. Dicey's 19th-century treatise on the British Constitution said that there was no need for an independent doctrine of Free Speech or Freedom of the Press because British law never had (at least, not in the then-recent history) and never would attempt to suppress speech as speech, or to single out newspapers as such. Libel, defamation, copyright and other so-called limitations on Free Speech aren't limitations at all because Free Speech isn't about freedom from the consequences of speech or prohibiting the government from remedying ill effects of speech or restricting them from activities that may incidentally limit speech. Those so-called limitations apply equally to everybody, so how could they operate to suppress particular ideas, opinions, or methods of communication? Likewise, Copyright doesn't favor anyone or any idea in particular, so it's not injurious to Free Speech, either.
So why did the Americans feel the need to singularly identify Free Speech and Freedom of the Press? Because continental Europe, and France in particular, had a history of laws that specifically and more strictly regulated the press, and regulated or prohibited particular opinions and ideas. Singling out Free Speech and Freedom of the Press was a way to explicitly reject the continental European approach. Remember, many colonists expressed the view that the enumeration of these and other rights in the Federal and State constitutions was, technically speaking, unnecessary because they were, strictly speaking, already protected by traditional legal doctrines and by the structures of government. The Bill of Rights was a boots & suspenders approach to constitutional law making.
None of this is to say that Parliament didn't pass laws that had the effect of limiting free speech. But how they did so mattered. Note that Free Speech and Freedom of the Press rights were also expressly put into many State constitutions. For well over a hundred years States regularly passed laws that heavily suppressed speech, but they were almost always upheld by State courts because the laws were expressed in terms of general applicability. In modern terminology they were "facially neutral", and there didn't exist a theory of judicial power that permitted courts to look beyond the face of the laws. (At least, not a theory that was widely held or that was thought useful to apply to speech issues.) And courts were far more credulous of State arguments that their laws were trying to prevent violence and mobs.
It wouldn't be until the 20th century that legal interpretations began to shift. Justices Brandeis and then Holmes propounded a novel (even radical) theory of Free Speech which demanded stricter scrutiny of laws and their effect on speech. It's adoption and application by SCOTUS has unfolded over the past nearly 100 years. This process continues today; scrutiny of laws effecting speech has become stricter and stricter every decade, even every year it seems. Moreover, what constitutes speech has expanded dramatically.
Make no mistake: Free Speech as understood in America today, and as defined by modern jurisprudence, is absolutely not an originalist interpretation of the constitution. If you like your modern Free Speech rights (as I do), don't thank the Founders; thank Brandeis and Holmes and their judicial activism.