If a "home theater" projector claims to be HD or 2K then it should be the native 1080p. If it is referred to as a "business" projector then check if the stats claim to support the 1920x1080 as a valid resolution (some do but most top out at WXGA or 1280x800).
Also be sure to check the lumens as they will effect the room lighting and the max size you can project and still have a clear image. A home theater projector for 16:9 images at 1500 lumens will need to be in a relatively dark room or at a smaller "screen size" of 90" or less where a projector at 4000 lumens will be clear at normal lighting at 120".
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