Novosti kosmonavtiki obtained an official confirmation from NPO PM, manufacturer of the Strela/Gonets series communication satellites, that the three satellites launched on May 23, 2008 are not Gonets-M satellites.
That explains why the satellites received Cosmos designations and not Gonets-M numbers. They are most likely part of the military counterpart of the Gonets-DM communication system. This system, which is replacing the old Strela-3, is probably what is known as Rodnik.
The difference between the military and civilian satellites is unlikely to be significant - NPO PM at some point referred to the spacecraft launched in May 2008 as Gonets-M. Still, designations certainly matter, so I corrected the May entry that described the launch.
The first launch of satellites of both new systems took place on December 21, 2005 - one satellite in that launch was Gonets-M No. 1, the other apparently was the first Rodnik. If that was the case, then the Cosmos satellites launched on May 23, 2008 continued deployment of Rodnik constellation. A launch of three Gonets-M satellites is scheduled for 2009.