Yes, "complete" in that case refers to both success and failures (at least in my experience). A feature request might be a good thing in this case, if you make use of the messages frequently and it would be helpful to differentiate.
@bvrooman Yes, we use the messages all the time. The policy in question was a caching policy say Adobe Reader. I have a policy that caches the installer then displays a message to the user to let them know they can install it (the cached version) from Self Service. That message showed up on a test machine even though the policy was not present in Self Service. I started digging into the install policy to see what was going on. Finding nothing, I finally moved over to the caching policy only to see the download had failed.
So yes, it that case, it would be beneficial to have a separate message depending on success or failure.
Think I will make that a feature request. Thanks for your input.