I agree with Navy. When I hear the word remastered I never think of pure HD. Though I would rather watch some of the old tv shows remastered than the typical sd.
For Ultra HD, movies are either shot in 4K (using 4K or 8K cameras), or they are remastered (from original film).
By "Remastering" they mean scanning/digitizing film to 4K (or 8K) frame by frame and then polishing each frame. It's a painstaking process. Lawrence of Arabia has taken nearly three years...