"Original cut" refers to the 1977 version. We have:
The 1977 release
The redone 1977 release which adds the "New Hope" moniker to fit with The Empire Strikes Back and its opening crawl which foreshadowed the twist by listing itself as "Episode V" hinting at a large backstory
The Special Edition, 1997, which adds new effects, a deleted scene, and introduces the running theme of the 'Han Shot First" scene being altered in some way or manner
The 2004 DVD version, same as 1997 but with botched colour timing and a new model for Jabba during the reinserted scene
The 2011 Blu-ray release, same but with a more comical sound for Obi-Wan's faux Krayt yell
And the 2019 Disney Plus/Blu-Ray rerelease, which is notable for having Greedo get the last word.
When we say "original cut", we're referring to the 1977 version, with or without 'New Hope' moniker.