I'm not sure these are documented so adding here:
Content status message of successfully distributed content is the normal status when you deploy content to a DP
Content status message of successfully processed content on DP is the status when you validate content on a DP
Content status message of content was distributed to DP is when you redistribute content to the DP.
Every time I do a CM Risk Assessment (RaaS) for a customer I have to remember the various versions of CM2012 clients that are out there. Here is a compiled list so I'll know where to find it (and maybe you will too!) :-)