There are two foreign intelligence services in todays Russia: SVR and GRU. The first one is the Russian Foreign Intelligence Service. It is the former First Chief Directorate of the Soviet era KGB, which has managed intelligence for decades. Its activities are well known throughout the world.
The second one is the GRU, Russian military intelligence. It is a part of the Defense Ministry. Its full name is much longer (The Chief Intelligence Directorate of the General Staff of the Russian Army). GRU has retained its Soviet era name, and just about everything else. GRU is seen as a living relic of the Soviet times. That is why GRU is so much more secretive than the "Westernized" SVR. GRU officers are considered more patriotic (and old school) than those of the KGB/SVR. During the Cold War, there were fewer GRU defectors, still a point of pride in the GRU. GRU prefers to stay in the shadows. Western writers have not written many books about GRU, compared to the KGB. This is largely because GRU keeps its secrets better, and, in the West, is considered an obscure part of Russian intelligence.
Both GRU (Russian Military Intelligence) and SVR (Russian Foreign Intelligence Service) perform the same functions: Political Intelligence, Scientific and Technical Intelligence (industrial espionage) and Illegal Intelligence. Because of this, the two agencies have a very real rivalry going.
But there was, and remains, one area where only the SVR (and its predecessor, the KGB) participates; running counter-intelligence abroad. This was long a KGB monopoly because it was the KGB's job to make sure the armed forces remained loyal, and GRU was, and is, very much a part of the armed forces.
Thus when the GRU officers are working abroad, they are monitored by Directorate K (counter-intelligence) of the SVR. Those who serve inside Russia, are watched by the Directorate of Military Counter-Intelligence (The Third Directorate) of the FSB (Federal Security Service, inheritor to the KGB). Interestingly, in the Soviet period, it was also called the Third Directorate. It is not a coincidence but a continuation of the Soviet tradition. The Third Directorate of the FSB is still assigned to monitor Defense Ministry, of which the GRU is a part. The head of GRU does not even report directly to the Russian President. GRU reports have to go through the Head of the General Staff and the Defense Minister before reaching the top man. Thus GRU is very much number two in the Russian foreign intelligence business. As Number 2, they tend to try harder, and consider themselves more elite than those wimps over at SVR.
On the other hand, there also is one function monopolized by the GRU; battlefield intelligence. The battlefield intelligence is run in peacetime as well. For example, in preparation for future wars, the GRU sets up illegal weapon and ammunition dumps in the territory of many foreign countries. This is a risky operation. It usually involves groups of junior Russian diplomats secretly going into rural areas to bury rifles, machine-guns and other weapons. They have to do this discreetly and in a hurry, to avoid detection by the local counterintelligence service. It is considered a hard job.
Western analysts regard the GRU the most closed Russian intelligence service partly because it does not even manage its own press relations. That's because GRU is one of many components of the Defense Ministry, and is not eligible to have its own press relations staff. The FSB and SVR are higher up in the government pecking order, and entitled to their own press relations operations. Formally, GRU is nothing but one of the numerous Chief Directorates of the General Staff of the Defense Ministry. It does not even report directly to the Minister of Defense. That is why, those foreign journalists who have questions about GRU, must address them to the Press Service of Russian Defense Ministry. The questions are often handled by some press aide who knows little about intelligence work, while FSB and SVR press people are very well informed. So foreign journalists tend to seek out the SVR press department when seeking information on Russian intel operations.
During the Second World War, GRU worked in close contact with the NKVD, the predecessor of the KGB. For example, in March, 1941, both intelligence services jointly carried out a successful operation aimed at overthrowing the pro-German government of Yugoslavia. During the entire war, GRU and NKVD were managing a joint network of foreign agents in Europe. The current system of two separate intelligence services, competing with each other, only came about in the 1950s, after Stalins death. It was done by the Central Committee of the Communist Party in order to secure itself from the coup inspired by either intelligence service. Thus the GRU not only competes with the SVR, it is supposed to keep an eye on the SVR, for signs of disloyalty.
In Soviet times, although the GRU was monitored by the KGB, both organizations reported to the Central Committee of the Communist Party. In case of emergency, the Central Committee could control the KGB using the GRU. The communists believed it best that someone guards the guards. Nowadays, GRU does not monitor the SVR anymore. GRU, the military and the rest of Russia, are all subordinate to the FSB/SVR.
The SVR has more money and resources. It's long been like that, and the GRU has developed a tradition of getting by on very little. GRU methods are considered more aggressive and crude than those of the SVR. GRU operatives tend to think they are at war even at the peacetime. Thus the SVR assigns its officers to do some job in the form of tasks, not orders. The task is not supposed to be necessarily accomplished, while the order is to be carried out by all means. The GRU prefers ordering, and expects results no matter what.
In the GRU nobody cares how their officers obtain secret information (like parts of missiles and other weapons). They may even buy it legally or semi-legally or even steal. The SVR officers are not allowed to do so. They are supposed to use foreign collaborators for it. In the GRU, you just go get it.