Conspiracy requires active participation in an act (and multiple people). .Conspiracy to riot involves planning acts that, if undertaken, would result in a breach of the peace. Conspiracy convictions usually require the defendant to have undertaken an overt act in furtherance of their plan. In other words, the words itself are not enough. Driving someone to the riot, buying the gun, etc. could be the act that must be combined with the words.
And, inciting to riot is a crime that involves more than just words. Note the definition in the federal statute: "As used in this chapter, the term “to incite a riot”, or “to organize, promote, encourage, participate in, or carry on a riot”, includes, but is not limited to, urging or instigating other persons to riot, but shall not be deemed to mean the mere oral or written (1) advocacy of ideas or (2) expression of belief, not involving advocacy of any act or acts of violence or assertion of the rightness of, or the right to commit, any such act or acts." 18 U.S. Code § 2102
The current test for what speech can be called inciting a riot (and this is the case that I think will get the present suicide case overturned) comes out of a 1969 Supreme Court case... In 1964, an Ohio Klansman named Clarence Brandenburg held a “rally” on a private farm—attended by 12 KKK members —and invited a TV news crew. They donned robes, burned a cross, sang a Klan song, and then heard a largely incoherent address by Brandenburg, who said, “We're not a revengent organization, but if our President, our Congress, our Supreme Court, continues to suppress the white, Caucasian race, it's possible that there might have to be some revengeance taken.” Brandenburg was convicted of violating an Ohio state law that banned “advocating ... the duty, necessity, or propriety of crime, sabotage, violence, or unlawful methods of terrorism as a means of accomplishing industrial or political reform...” In this case the Justices used Brandenburg to signal that they would not tolerate the use of “incitement” as an excuse to shut down speech, even if offensive or violent. The Court held that the First Amendment protected even speech that urged breaking the law—unless it was “directed to inciting or producing imminent lawless action and is likely to incite or produce such action.” What that means is most incitement cases never happen. “Directed to” means that the speaker must have intended to cause violence; “likely to” means that there must be a true danger of violence; and “imminent” means that the danger must exist at the moment of the speech—not days or even minutes later.