The April 26th launch is reported to be conducted as part of the "Arbalet" program (switch to Russian language to see the report). It is hard to tell what this program is, but the report also says that the launch was related to "combat readiness," so it may be that "Arbalet" is just a program that includes regular missile launches to train the crews and check all the systems.
The second launch, on May 20th, appears to be more interesting. The report says that it was part of the "state flight test program (Program "Liner")." The report then refers to the missile as "Liner SLBM," not "Sineva." It adds that the Liner missile was developed by the Makeyev Design Bureau and produced by the Krasnoyarsk Machine-Building Plant. It looks like the missile tested on May 20th was not a regular Sineva, although in the official statement of the ministry of defense the missile was referred to as Sineva.
As one would expect, there is very little information about the Liner program (although it was mentioned a while ago as a project the Makeyev Design Bureau was working on). One possibility, which would probably explain both the differences and similarities is that Liner is a Sineva that carries more than four warheads. Back in the 1980s, the original R-29RM missile was tested with four and ten warheads. The ten-warhead version of the missile, however, was never deployed. It shouldn't be very difficult to go back and revive that old project. Maybe that's what the Liner project is. I hope we'll see more details coming out soon.