So I know this may turn into a large debate, but I just want to address the question if video game companies could sue the people saying that they are causing mass shootings for slander or defamation? If they could, do they not do it because they are unlikely to win or are there other reasons? Also I have very little background in law so please explain it in detail, I'm not even sure what the difference between the two are. Please stay on topic of the question.
Such a lawsuit would be unsuccessful in the United States, given the numerous barriers imposed by the First Amendment.
First, a plaintiff can only win a defamation case if it proves that the defamatory statement was false. If a statement cannot be proven false, it is legally considered a statement of opinion, which is protected by the First Amendment. Milkovich v. Lorain Journal Co., 497 U.S. 1, 19 (1990) ("[A] statement on matters of public concern must be provable as false before there can be liability under state defamation law.")
Second, statements about public figures or matters of public concern can only be the basis of defamation liability if the plaintiff can prove "actual malice," which means that the defendant either knew what he was saying was false or had a "a high degree of awareness of . . . the probable falsity" of his statements. Harte-Hanks Communs. v. Connaughton, 491 U.S. 657 (1989).
Even with actual malice regarding statements of fact, the defamatory statement is considered in context, not in isolation. So a newspaper headline that is incorrect would probably not result in liability if the full article was correct. And the question is not whether that statement of fact, considered in context, is literally false, but rather whether the "sting" or "gist" of the statement was false. Air Wisconsin Airlines Corp. v. Hoeper, 571 U.S. 237, 247 (2014) ("A statement is not considered false unless it would have a different effect on the mind of the reader from that which the pleaded truth would have produced.").
For example, saying "John shot his wife" would probably not be defamatory if John shot at his wife and missed, or if he beat her unconscious with a gun, or even if he stabbed or poisoned her. John's reputation is damaged because he tried to kill his wife, not because of the precise way he did it.
Applied to video-game manufacturers, these rules effectively kill a defamation action.
First, they have to prove both (a) that it's possible to say whether video games cause mass shootings; and (b) that video games definitely don't cause mass shootings. That requirement probably kills the case already, because that research doesn't exist. Even if it did, the manufacturers would then need to prove actual malice, meaning either that the defendant knew about that research, or that the defendant knew that what they were saying was probably false.
I don't know how anyone could prove all that, and even if they did, they'd still have questions about the "sting" and broader context of the statements, making this case a serious loser.
While I doubt that video games are causing mass shootings, I also doubt that the people who say otherwise believe they are correct. Generally speaking, the First Amendment protects people who make mistakes. New York Times Co. v. Sullivan, 376 U.S. 254, 271–72 (1964) ("Erroneous statement is inevitable in free debate, and ... it must be protected if the freedoms of expression are to have the breathing space that they need to survive.")