Treason: Treason is explicitly defined in the Constitution (and all other definitions are explicitly rejected): levying war against the United States or aiding and abetting their enemies. It is not something that applies outside explicitly declared hostilities, and anyone who uses it in this context is dangerously ignorant.
Sedition: Because the United States is designed to be a free society, the only actual crime of sedition is a conspiracy crime: conspiracy to overthrow, put down, or destroy by force the government of the United States, to levy war against it or oppose by force its authority, to delay by force the execution of its laws, or to take by force any of its property contrary to its authority. It is a very difficult crime to establish, because you need to establish (1) that there was an actual conspiracy (one person acting alone is not enough, a mob of people acting without joining in a plan is not enough) (2) specifically to do one of the things listed above. A number of people at the January 6 event, not all, have been charged with sedition; most of them probably will not be convicted of it. In the United States, you can go as far as calling for the overthrow of the government and it's not sedition unless in doing so you try to implement a practical plan for it. A free society is inconsistent with the very idea of easily labeling and punishing people as seditious; anyone who uses the term in any context without being very careful to argue that the evidence does, in fact, establish that sedition in the above sense occurred, is utterly dangerous and morally contemptible. No one who takes democracy or republican principles of government to be important would ever throw around the word without backing up the use, and particularly would not ever use it as political rhetoric. If you find anyone doing so, it should raise red flags.
Insurrection: Insurrection is a weird word. It sounds like the beginning of a revolution (and is often paired with either that or 'rebellion'), but it includes any armed uprising against the authority of the government. Most people involved in the protests on January 6 were unarmed; indeed, most people who actually trespassed on Capitol grounds were unarmed. A few were armed but don't seem to have made even threatening use of their arms. None of these people would count as insurrectionists. There were others, although I can't find any record of anyone from January 6 who has been charged with insurrection or similar crime, although admittedly, it's not as if the reporting on it has been very good. (Most have been charged with civil disorder and entering restricted property.) An insurrection doesn't always mean much; depending on context, a few armed people chasing federal agents off their property at gunpoint or forcibly seizing government property could be insurrection, even if there was never any impulse beyond that. It's a less objectionable word for the events in question than 'sedition', although it seems to me that it's often being used more for rhetorical effect than anything else.
Trump, of course, was impeached on one count of inciting insurrection. I'm very skeptical of the idea that anything Trump did actually meets the legal definition of incitement, which is very restricted for the same reason the legal definition of sedition is. But impeachment is not indictment; it's a political, not a legal, judicial act, and whether he is convicted will simply depend on whether Senators think he had some prior knowledge of what his comments on January 6 would lead to and whether they think it politically a good precedent to set.
