As we are limited in space, below are a few ideas concerning both Russian special forces and US special forces to help get you started.
One counter-terrorism unit is called Russia's Alpha Group, which is officially called Directorate "A" of the FSB (Federal Security Service) Special Purpose Center. The elite task force was constructed by the KGB under the Soviet Union in 1974 but is still very much in service today. Under the Soviet Union, the Alpha Group was especially used to handle Soviet Union deserters, as well as hostage situations. Among Alpha Group's noteworthy operations is the capture of those who hijacked Aeroflot flight 6833. In 1983, members of the Alpha Group stormed the airplane in flight, killing three out of six of the hijackers and capturing the rest. Another noteworthy operation is called Operation Storm-333. In 1979, Alpha stormed the Tajbeg Palace in Afghanistan and assassinated President Hafizullah Amin, whom the Soviet Union had supported but turned against. Alpha also captured the key government institutions, Ministry of the Interior and Ministry of Defense, in Kabul and replaced Amin with Babrak Karmal.
Another unit that has been used for counter-terrorism operations is the U.S. Navy's Sea, Air, Land Teams (SEALs), which are part of the Naval Special Warfare Command and the United States Operations Command. The SEALs have been particularly active in the current War on Terror, and one memorable operation they conducted recently was the Battle of Takur Ghar in 2002. SEAL teams MAKO 30 and MAKO 21 were deployed to take Shahi-Kot Valley, an area intelligence had already identified as being densely occupied by the Taliban and al-Qaeda. The two teams also needed to take Takur Ghar peak as a point to survey activity in Shahi Kot Valley. After several difficulties concerning landing on and taking Takur Ghar, MAKO 30 requested back-up from a Ranger quick-reaction force composed of 19 Rangers, a Tactical Air Control Party, and a 3-man USAF special tactics team. The Rangers were able to land but 2,000 ft away from the peak, resulting in the Rangers needing to climb to the peak, an exhausting, 2-hour long process. Once on the peak, the Rangers were able to kill an estimated 200 Taliban members and take the hill.
Similarities in the missions of both Alpha and the SEALs have to do with the fact that both were employed to either take over and control a government or insurgent. Both were also employed to perform difficult feats, such as storm a moving plane or storm a mountain peak that is already heavy with enemy fire. One difference can be seen in the fact that the SEALs were employed for a military operation, while Alpha was used more frequently at home to deal with Soviet Union deserters or also used to deal with any government that posed a threat to the Soviet Union.