In the United States, all speech is considered to be protected until proven otherwise. In a criminal case, the defense has no burden of proof that the statement was made as a form of a threat. Thus, the Prosecution must show that the speech was unacceptable. As the case of Watts v. The United States decided, a True Threat only if the messenger intended it to be interpreted as a threat and the audience reacted as such. In the case of Watts, who was opposed to the Vietnam war and the draft and said at a public protest that if the nation ever made him carry a rifle, he would endeavor to make sure President Lyndon Johnson was the first person in his sights, and then mimed shooting a gun. He was arrested by the Secret Service for making a threat against the President.
While the supreme court, on appeal, found that the law against threatening the life of the President was constitutional, but it did not make Watts statements illegal. Watts maintained that he was merely joking, and admitted it was probably not the best joke to make, thus showing his intent was not malicious, and the fact that the audience was largely laughing and applauding and cheering, meant that it was not seen as a threat by the reasonable person.
This is not an either or situation. A true threat must be both intended by the speaker to threaten someone or something AND must be understood by the recipient(s) as a threat in order for it to be a true threat.
Take for the situation a fake bomb scare called into emergency services. The speaker would know that any threat made in a 911 call will be understood as a threat, and thus, cannot joke with an on duty 911 operator. There is no reasonable way to interpret a call of a bomb threat to 911 as a joke, and thus the intent is to make a threat, even though no lives are ever in danger.
However, if we look at the Kathy Griffon picture of her holding President Trump's severed head, we do understand the likely intended message was not a threat to kill the president, even though the audience largely was not amused. She did get investigated by the Secrete Service, but they found no evidence to say that the joke was nothing more than a very bad joke that was not intended to actually threaten, but just mock (Most Americans do not appreciate jokes about killing the President, even if they do not like the current president. Its one of the very few things Americans do agree on.).
The Prosecution will have to prove that your intention was either to threaten or make the listener believe the false threat AND the listener must understand it to be a threat.
Because all restrictions must be context neutral, no specific statements or practices are outright labeled as a threat. You can in fact shout Fire in a Crowded theater without being arrested for making a threat. After all, scene in the play called for the actor to announce the fire. And when in doubt, the speech should be protected.
To answer why the intent of the speaker, I'd like to use my go favorite lawyer movie, "My Cousin Vinny" to show how context when related to speech is very critical.
The cousin of Vinny (Bill) is from Brooklyn and is charged with a murder of a shop clerk he did not commit in rural Alabama (The viewer knows this). The cousin believes that he was arrested for an honest mistake petty theft of a can of tuna from the same store (he was probably the last person to see the clerk alive). When he tries to confess to taking the tuna, the sheriff believes he was confessing to the murder of the clerk, and when the sheriff gets impatient, we get to this exchange:
Sheriff: When did you shoot him?
Sheriff: At what point did you shoot the clerk?
Bill (confused): I shot the clerk?
Sheriff: Yes, when did you shoot him?
Bill (still processing the question): I shot the clerk?!
Officer: Dean, we need you out here!
Sheriff: I'm right in the middle of a damn confession here! (Sheriff
and Deputy leave room. Bill realizes...)
Bill: WHOA!!! Wait a minute!!
It's important to state that there is no malicious on this part. My Cousin Vinny was praised for it's ability to show that the witnesses for the prosecution were not corrupt country hicks that sleep with their sisters, as the movie puts it in more crass language. The sheriff does actually help Vinny win the case at a point where he makes it clear that it is not part of his job and once new evidence comes to light the prosecution does admit it got it wrong (he's even given a sympathetic story to show he's not a bad guy). In the above scene, Bill is clearly trying to work through what the sheriff asked him and is quite floored by the accusation that is made. The sheriff believes he's confessing to the murder, not petty theft and thinks Bill is stalling, and both are unfamiliar with each others accents. Furthering the problem an officer pulls the sheriff away as Bill comes to the realization of the gravity of the situation he's in but the Sheriff is distracted by other matters and doesn't catch these changes in attitude going on. And later in this movie, the fruits of this scene come to bear when the sheriff is testifying in court
Sheriff: (dryly without any hint of emotion) I asked him if he did it, and he said 'I shot the clerk.' I asked him again, and again he said 'I shot the clerk.'
The sheriff, in complete earnest, has turned Bill's questions made in a state of utter confusion to be statements of fact. An emotionless quotation of an utterance is quite plausible in court. Even if the sheriff was personally out to get Bill, he's been in court enough times to testify to all manner of crimes that he has developed a dry read of statements because he's relying on the facts and facts alone.
This scene is usually used to show what they mean by "Anything you say can and will be used against you" during Miranda reads. In fact, because of rules on Hearsay, an arresting officer can only testify to statements you made that are injurious to you... if you say over and over that You are Innocent, he cannot attest to those statements during trial.
But we can also use it to show why context and intent of speech is important. In this case, the difference in punctuation of the spoken words "I shot the clerk?!" and "I shot the Clerk." are so vast that in the court of law, it's the difference between innocence and guilt. And because punctuation is not heard in an English statement, things such as tone are used to convey the question. You probably even read the two quoted statements in completely different tones, even though they were side by side.
Again, it's important to know that the sheriff did not deliberately misrepresent Bill's statement. He gave an accurate report of the statement as he recalled it. The analysis of the error was not really explored because the charge was for murder, not a true threat, so free speech issues weren't discussed much in that issue. However, had this been a free speech error, the misread is a critical mistake that could have flipped the case against Bill despite the fact that Bill never would have confessed had he known ahead of time that he was under arrest for murder. Here, it only put him up for the death penalty.
And as a final note, I did leave something out on Watts: He did in fact commit a crime that night. Watts was found in possession of marijuana during a search related to his arrest for making a threat against the President. He was found guilty of the crime well before his case was decided by the Supreme Court. When the court ruled in his favor, this case was overturned by lower courts because the cause for the search (the arrest for threatening the president) was no longer a valid arrest, and thus the probable cause for the search and the evidence was only found on that justification. Just to stress how absolutely critical a speaker's intended meaning is to a case of True Threat.