Semantics. Without a picture, we can't be sure that what you mean by "offset printing" is the same as what we are thinking. When I hear "offset printing error," it means the paper sheet failed to enter the press and the back cylinder is stamped with ink. When the next paper feeds correctly, you get a mirror image on the back of the note. As @BStrauss3 and @Coinfrog said, the term "offset printing" refers to the process by which ink is transferred from the plate to the rubber and then to the paper instead of directly stamping the paper with the plate. That's why an offset printing error comes out as I described above (mirrored) and isn't an offset (off to one side) looking image per se.
If you mean offset as in "off to one side" then that may be a misaligned overprint (the seals and serial numbers are "offset"). That can also be an error if the misalignment is significant. There are also faulty alignments where the printed design is shifted.