The reason for the two most powerful positions any country can have which exists in Russia is because of the fact that the country practices a semi-presidential system of government. The highest political office in Russia is the office of the president. The president of Russia is the head of the government and that of the state.
The prime minister and other members of the executive are appointed by the president. On the other hand, the prime minister is serving as the vice president, just like how we have it in other countries. Although, the executive arm of the government is headed by both the president of Russia and the prime minister, the president of Russia seems to have more constitutional roles and responsibilities compared to the prime minister.
The nomination of the officers and other members of the executive is done by the prime minister, while it is the President's duty to approve anybody nominated by the prime minister. The implementation of the domestic policy of the country is done by the prime minister.