Quoting Wikipedia[1] quoting the US Supreme Court,

The thread running through all these cases is that prior restraints on speech and publication are the most serious and the least tolerable infringement on First Amendment rights. A criminal penalty or a judgment in a defamation case is subject to the whole panoply of protections afforded by deferring the impact of the judgment until all avenues of appellate review have been exhausted. Only after judgment has become final, correct or otherwise, does the law's sanction become fully operative.

A prior restraint, by contrast and by definition, has an immediate and irreversible sanction. If it can be said that a threat of criminal or civil sanctions after publication "chills" speech, prior restraint "freezes" it at least for the time.

[1] https://en.wikipedia.org/wiki/Prior_restraint#Judicial_view