The other sense is much harder to define. The concept of the "marketplace of ideas". Essentially that ideas should be heard out and debated. This is where things get debated, because people will often call what they don't like an attempt to censure free speech.
For example, if people protest someone's message, that still clearly fits under the "free speech" category of the first definition. However, people will debate what that means under the second.
Liberdon is a Mastodon instance for libertarians, ancaps, anarchists, voluntaryists, agorists, etc to sound off without fear of reprisal from jack or zuck. It was created in the wake of the Great Twitter Cullings of 2018, when a number of prominent libertarian accounts were suspended or banned.