Search example.

        {
          "disc-count": 0,
          "format": "Digital Media",
          "track-count": 9
        }

Lookup example.

     {
      "format": "Digital Media",
      "format-id": "907a28d9-b3b2-3ef6-89a8-7b18d91d4794",
      "position": 1,
      "title": "",
      "track-count": 9
    }

1. The search output includes disc-count (the number of disc IDs attached to the medium), which is fine, but it probably should not be outputted for formats that cannot have disc IDs.
2. AFAICT, lookups never output disc-count – this property is not outputted by musicbrainz-server at all.
3. The search output is missing format-id, position, and title.