His successor Putin spent eight years bringing Russia out of the "mess" and back in "order" and now the country is regaining strength. That has come to be known as the "Putin era" and the Medvedev-Putin pairing will carry on the mission that Putin started.
Russia is a nation in transformation, which is inevitable in that it has abandoned the Soviet-style socialism without converting to the European-US-style social model and shares some of China's reform concepts, but its format is different from China's. Putin once said Russia's thinking "combines organically the common values of the humankind with Russia's time-tested traditional values". This is in a way inevitable, too.
The fourth is generality and particularity. Russia normally follows a general presidential election process but each winner's background and condition were different. Medvedev succeeded the Russian presidency in a situation totally different from Putin's when he became president of Russia. Where Putin dumped the mess left by Yeltsin and started anew, Medvedev found himself marching ahead with Putin on the path chosen by his predecessor.
For Medvedev it is "following Putin's rule" whereas what Putin did is continuation, improvement and completion. Since the previous president could not achieve perfect score and left behind some problems, his successor must make policy adjustments and corrections, which does not mean Medvedev will do anything against Putin personally but that both of them will shoulder the task.
The Russian prime minister's first and foremost responsibility is the economy, as is generally the case throughout the world. For Putin, he is also expected to have a bigger say than usual on security strategy and foreign relations because of his experience and international clout. That is something former Russian prime ministers did not have and has been confirmed repeatedly by Putin's frequent trips overseas and the way he spoke about international hot issues.
The fifth is commonality and individuality. Putin and Medvedev share something in common - they both shoulder the responsibility of directing Russia's rejuvenation. Meanwhile, they each have his own personal style and character as well, though that does not negate their commonality.
It is not hard to understand why some media entities are so obsessed with the differences and disagreements between Putin and Medvedev.