The line between genres of cinema is often blurry and almost always pointless. People just want to know what type of film they're getting into, but attempting to divide art by the feeling it inspires will always be a matter of subjective taste. While the divisions are unclear, it's interesting to see one genre attempt tricks from another and occasionally even do them better.
Generally, the biggest difference between a horror movie and an action movie is the capability of the protagonist in comparison to the antagonist. An action movie protagonist can be faced with seemingly impossible odds and fight back to win the day, but a horror movie protagonist is typically barely able to run away. Blending the two, however, often creates something even more gripping.
Overlord
War horror is a unique subgenre that adds a second layer of nightmarish supernatural evil to the existing unbearable torment of combat. Some accomplish that with heavily metaphorical psychological hauntings, but others go right for the throat by warping human flesh to better resemble its monstrous insides. Overlord sees a small team of US Army soldiers accidentally stumble upon an underground bunker in which Nazi scientists are hard at work creating monsters. This small unit must fight their way through, against armed Nazis and mutated super soldiers. This is unquestionably a frightening film, packed with gore and unflinching violence, but it's also a film about fighting back. There's not a lot of hidden depth, but there is a lot of fun and unrestrained violence.
The Collection
In the late 2000s, screenwriters Patrick Melton and Marcus Dunstan pitched a film then called The Midnight Man. It was proposed as a prequel to the Saw franchise, but that idea wasn't accepted, so the film was reworked into a slasher that feels extremely derivative of the Saw franchise. That 2009 film, The Collector, tells the tale of Arkin, a thief who breaks into a wealthy family's home to discover that a mysterious and powerful serial killer is in there with him. The 2012 sequel, The Collection, concerns Arkin and a team of mercenaries attacking the killer's home base for revenge. Neither film is perfect, but the sequel sees the heroes enter a variety of violent confrontations with the killer. Traps are common, but much of the second film sees Arkin fight the occasionally omnipotent killer in pulse-pounding combat that feels like a legitimate escalation of the first film's horror.
I Saw the Devil
On the subject of genre cross-over, where does a thriller step into the realm of horror? Kim Jee-woon's 2010 South Korean masterpieceI Saw the Devil tests that divide with force and fits comfortably into both camps. Oldboy star Choi Min-sik portrays a sadistic serial killer who abducts and butchers a pregnant woman after a chance encounter. Unbeknownst to him, the victim's fiancé is an elite intelligence agent who immediately swears revenge. Lee Byung-hun takes the lead role as a man driven to gradually deeper levels of depravity in pursuit of vengeance. This vengeance is imminently cathartic in every outing, the cat and mouse chase as Lee comes inches from killing his prey, only to back away to prepare some worse fate is maddeningly tense. Some of the film's physical exchanges would be right at home with the gorier martial arts movies. It's an incredibly tough watch, but it's well worth it.
Blood Red Sky
Set almost entirely on a transatlantic passenger flight, Peter Thorwarth's Blood Red Sky is one of those simple horror premises that provokes questions like "how hasn't this been done yet?" A violent group of hijackers takes over an otherwise uneventful plane, only to discover that an unassuming passenger is hiding an extremely dangerous secret. That secret, revealed about halfway through the film or immediately in its trailer, is a recently obtained case of vampirism. A vampire versus terrorists action horror film in a plane in flight is a perfect tense nightmare, and the film is happy to explore every angle. Violence in the model of 30 Days of Night meets a more grounded portrayal of modern terrorism, and it is a gripping series of physical exchanges.
Mandy
Anyone who has seen this film was waiting for its place on this list. Panos Cosmatos's 2018 unhinged psychedelic nightmare experience blends music video and slasher film to create something truly unique. Elements of Mandy eschew the bounds of cinema and trend into a tone poem where the tone is drug-fueled bloodlust. The plot follows Red, portrayed by Nicolas Cage, a man living a simple happy life with his girlfriend Mandy until their idyllic existence is ruined by local cult leader Jeremiah. After mourning Mandy's death, Red begins a tormented vengeance quest that gradually undoes reality around him. The action is often far and away the most visually gripping imagery in the genre. There are decent action films that could still stand to take a few notes from Mandy.