2K resolution is a generic term for display devices or content having horizontal resolution on the order of 2,000 pixels. DCI or the Digital Cinema Initiatives defines 2K resolution standard as 2048×1080, or 1998x1080 as Flat presentation.
In the movie projection industry, Digital Cinema Initiatives is the dominant standard for 2K output. In the digital film production chain, a resolution of 2048x1556 is often used for acquiring "open gate" or anamorphic input material, a resolution based on the historical resolution of scanned super 35mm film.
Occasionally, 1080p (Full HD or FHD) has been included into the 2K resolution definition. However, this appears to be incorrect consumer assumption, rather than official inclusion into the resolution terminology. Older and current media, web content, and books on video production and cinema references and definitions define 1080P and 2K resolutions as separate definitions and not the same.
1080p has the same vertical resolution as 2K Resolutions (1080 pixels), and 1080p can be utilized within the 2K resolution container. However 1080p has a smaller horizontal resolution below the ranged of 2K resolution formats.
According to official reference material, DCI and industry standards do not officially recognize 1080p as a 2K resolution in literature concerning 2K and 4K resolution.