It's quite rare, but yes , it has happened with Hollywood movies.
One example is Chaos (2005).
Chaos (2005)
Action, Crime, Drama Director:
Tony Giglio Stars: Jason Statham, Ryan Phillippe, Wesley Snipes
Distributed by:
Capitol Films, Lionsgate
Two cops, a rookie, and a grizzled vet, pursue an accomplished bank robber.
— Chaos (2005) , IMDB Crime, Horror, Thriller Director:
David DeFalco Stars:
Kevin Gage, Sage Stallone, Kelly K.C. Quann Distributed by: Dominion Entertainment, Dinsdale Releasing Two girls, looking to score some ecstasy at a rave, follow a young man to a house where terror awaits.
There, a gang of felons captures and torment the girls, drawing them into a nightmare of violence.
—
Chaos (2005) , IMDB The way Wikipedia disambiguates or distinguishes the two is by adding a distributor of the film in with the release date: Chaos (2005 Capitol film)
Chaos
(2005 Dominion film)
Incidentally, Wikipedia lists the Capitol film's release date as 2006, rather than 2005, based on a German release date.
Looking at the release dates for this film , you can see that this movie has been released in '05, '06, '07, '08
(in USA and UK) and '09, yet IMDB considers it a 2005 release because it was first released in 2005 in the UAE, which technically makes this fit your criteria.
Another piece of trivia: the Dominion film was first (August '05, versus Capitol's December '05).
movies.stackexchange.com/users/42655/Ghoti and Chips
Here is another example of the movies with same name and same release year.
Night Club (1989)
Genre:
Comedy Director: Sergio Corbucci Stars: Christian De Sica, Mara Venier,
Massimo Wertmüller
From IMDb, The nightlife of young carefree friends in a wonderful 60s
Rome Night Club (1989) Genre:
Drama Director: Michael Keusch Stars: Nicholas Hoppe, Elizabeth Kaitan, Ed Trotta
From IMDb, A young married couple try to convert an old warehouse into a nightclub, but face opposition from both the council and local mobsters.
movies.stackexchange.com/users/48608/Nog Shine
Another example is two of the adaptations of Jane Austen's Emma that came out in 1996, both which retained the name "Emma".
http://www.imdb.com/title/tt0118308/ http://www.imdb.com/title/tt0116191/
In this case, one of them was made for Television in the UK, while the other was made for theaters in the USA.
movies.stackexchange.com/users/42015/GendoIkari
In 1965, two movies about Jean Harlow, each named "Harlow" were released.
One with Carroll Baker and one with Carol Lynley.
There were two TV movies called 20,000 Leagues Under the Sea in 1997.
In addition to Steven Spielberg's 2005 War of the Worlds film, there were two direct-to-video retellings of the story that year.
movies.stackexchange.com/users/64413/Joe Schreck
Black Rain (1989)
Genre:
Drama Director: Shôhei Imamura Stars: Yoshiko Tanaka , Kazuo Kitamura, Etsuko Ichihara From IMDb, Mr and Mrs Shizuma, and their niece Yasuko, make their way through the ruins of Hiroshima, just after the atomic bomb has dropped.
Five years later, Yasuko is living with her aunt and uncle, and her senile grandmother, in a village containing many of the bomb survivors.
Yasuko does not appear to be affected by the bomb, but the Shizuma's are worried about her marriage prospects, as she could succumb to radiation sickness at any time.
Black Rain (1989)
Genre: Action, Crime, Thriller Director: Ridley Scott Stars:
Michael Douglas, Andy Garcia, Ken Takakura
From IMDb, Two NYC cops arrest a Yakuza member and must escort him when he's extradited to Japan.
movies.stackexchange.com/users/42844/Silver Bebs
I was thinking about the typical citation standard for referencing movies, where one writes the title and the release year, in the format " Title  (Release year)" e.g.  Jurassic Park  (1993).  This works quite well, except if there ever is a movie which has the same name as  another movie  that came out during  the same year .  Does there exist an example of two movies with the same name, and same release year?
Have there ever been movies with the same name, released in the same year?
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movies.stackexchange.com/questions/78328
movies.stackexchange.com/users/42655/Ghoti and Chips
There are a number of cases of films with the same name being released in the same year: Chaos (2005), Night Club (1989), Emma (1996), Black Rain (1989), among others. There many examples for movies realeased in the same year and under the same title
There many examples for movies realeased in the same year and under the same title