On a coreOS (899.15.0) machine, when I execute docker search and images I get the following results :
docker search private-registry:5000/
NAME      DESCRIPTION   STARS     OFFICIAL   AUTOMATED
docker images on the private registry machine:
REPOSITORY                                                      TAG                 IMAGE ID                                                           CREATED             VIRTUAL SIZE
nginx                                                           latest              e32087da8ee6dfa45221c48670fa9475f3d8a53a0e9ccabef4f741c62c77d49b   2 weeks ago         182.6 MB
registry                                                        0.9.1               facc02b3acf6f811e8eace6d07b34cd5ab687e926ac5b5231da93264b259f1a4   12 weeks ago        422.8 MB
<none>                                                          <none>              db81ebdc7ebd3d7aec05d4faa6f4c9c2e35954896e968bce2f90a9736485aa06   3 months ago        422.8 MB
...and a few more images
The reference for docker search mentions that it looks up on docker hub, but since I am specifying a specific registry here, I suppose it is looking up in the private repository.
I am not sure what is the difference between these two commands here and why the difference in results.