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I'm well aware of Carnival of Souls and Signs is no where near that style of filmmaking. Signs is an utter failure on so many levels, by the obvious horrible writing put in it's easy to tell the alien "threat" was thrown in last minute to make the movie more marketable. Signs is a family drama first and foremost, it becomes at most a suspense film second. There is no sense of macabre or dread in the so called atmosphere of Signs, at most the audience is left to question, "why are the aliens here and what do they want?" That is not horror as the audience does not know what they are there for, they don't know what the plan is. Not knowing the intentions of a "threat" is not horror but suspense.
What the audience is given is a family that has had this great tragedy forced upon them and we watch as they try to stay as a family and a once religious man questions faith. With occasional random scenes of aliens outside the window as a way to lie to the audience saying "oh by the way an alien invasion is going on so this is really a suspense movie." Your attempt at defending the jump scares did nothing but prove my point that they were there just to get a few seconds of a reaction, it added nothing to the supposed atmosphere that the defenders keep referring to and it does nothing to qualify as horror.
I do agree Saw was not a violent movie since all we really saw was an aftermath but Saw is far more horror than Signs as Saw lead you to believe death was inevitable for these characters. Whether the killer or not was the one who was actually going to kill them the audience was lead to believe they were going to die and could only hope they found a way out. Which is why Saw is one of those films that could go to either side. (I'm only referring to the first Saw movies as the sequels/series have become nothing more than a gimmick much like Friday the 13th and Nightmare on Elm Street.)
Going by your definition as to what can be considered horror and what is not isn't wrong and that's not the problem but people have decided that if they are scared or horrified by what they see then they're free to call it horror. Which is fine if we are just talking about opinions but it doesn't work that way for deciding what is and what is not horror.
Yes there are the blatant horror movies, then there are ones that have more going on that just person X hacking up random people. To give the best example in comparison to Signs, The Host is a movie that has its story and characters that can qualify as horror. Once again The Host has alot to do with a family drama but the story is about a family that is torn apart after a monster went on a rampage took several family members, while Signs is about a family and there just happens to be an alien invasion going on aswell.
There is alot to consider when deciding what genre a movie fits into, especially when looking into the context of the story, it's those things (and more) that separate the movies from horror, action, drama, etc. Not ones personal reaction to a movie or if happens to have minor themes that are from another genre.