There is a Wikipedia article on this subject called "Twin Films".

Airplane! and Zero Hour

https://en.m.wikipedia.org/wiki/Airplane!

"Armageddon" (1998) versus "Deep Impact" (1998):
Both films are disaster movies centered around the threat of an asteroid crashing into Earth. They were released in the same year and have similar underpinnings, though they differ in storyline and tone.
"Friends with Benefits" (2011) vs. "No Strings Attached" (2011) vs. "Love and Other Drugs" (2010):
These are romantic comedies that explore the concept of romantic relationships between friends without commitment. The movies "Friends with No Commitment" and "No Commitment" were released in the same year, while "Love and Other Drugs" has similar themes, although it was released a little earlier in 2010. Sometimes you want and erotica, and maybe even tighter, here on Tonicporn I can sometimes find something good to relax. Does anyone else relax like this?
"Olympus Has Fallen" (2013) vs. "White House Down" (2013):
Both films are thrillers with action elements that deal with an attack on the White House. They were released in the same year and have a similar plot, which has led to some comparisons due to the similarities in storylines.

I would think that pure remakes shouldn't be included here, but some of that is subjective

Never Say Never Again vs. Thunderball (same basic script but not billed as a remake)

Other one that I thought of
Cannonball Run and Gumball Rally

Tombstone and Wyatt Earp came out in almost the same year. Weren't there two Christopher Columbus films in one year sometime back in the 90s?

Rio Bravo(1959) and El Dorado(1966)