I think a lot of it comes from the post-modernist, genre-blurring tendencies that started in the 1970s and 80s and are becoming more pronounced as we go along.
For instance, back in the day, a 'Horror' film had to have a monster, and the monster had to be the result of supernatural forces. Thus vampires, werewolves, ghosts or demons. Even Frankensteins' monster was viewed as supernatural. because despite his claim to be a scientist, Frankensteins' laboratory was always shown to be more that of an alchemist or wizard than a scientist. If the monster had been created in a shiny modern lab, then the films would have been classed as SF. Dr Jekylls lab is shown in the same way.
Where the menace was merely human or animal, no matter how depraved, over-sized or hungry for humans, the film was described as a 'Thriller'.
The problem being that thrillers and horror movies share a lot of their DNA. Gore, suspense, jump scares and so forth. The same applies to a certain style of SF, such as Alien which has definite horror tropes, or the Predator movies which have much in common with thrillers or even adventure films.
So that I would class both Jaws and Silence of the Lambs as Thrillers in the same why that Psycho -one of the scariest films ever - is a thriller. Thrillers are, on the whole, regarded as being a cut above horror films as they can at least make a show of being realistic and often delve into psychological, cultural and social/family issues when creating both their villains and heroes.
Get Out and The Black Swan are both post-modern efforts which defy single-genre classification.
The Sixth Sense, however, is the classic reverse ghost/horror story in which the protagonist is revealed as being themsleves the ghost or monster. The Others is another example of this, while H P Lovecrafts' short story The Outsider is one of the best.
Film critics are notorious for preferring films that earn comment such as "a penetrating study of modern life" or "a searing protrait of a dysfunctional family", while the public quite often just wants something to enjoy without effort while munching popcorn. The Academy Awards, like it's British equivalent the BAFTAs, is forced to balance between popular opinion and critical approval, since their aim is to keep cinema recognised both as popular entertainment and a serious art form.
