Difficult enough to say In Russian, the word "spetsnaz" denotes special units (thanks, Cap). They are prepared for special, especially complex operations with small, usually forces. By subordination, one can distinguish special forces subordinate to the Ministry of Defense, special forces subordinate to paramilitary formations (gendarmerie, Internal Troops, border troops), special services (special forces of the FSB, CIA), and the police. Accordingly, the subordination and tasks differ - for example, the police special forces are more focused on suppressing mass riots, fighting heavily armed criminals, and releasing hostages. units of the Special Services can, depending on the direction of the special services (intelligence or counterintelligence), be used inside the country (counterterrorism) or abroad.
So, both the Russian Federation and the United States have a "full set" of special units - their have the armed forces of both countries, counterintelligence agencies (FSB and FBI, respectively), police. The difference, as I understand it, concerns mainly weapons and equipment, it is POSSIBLE in the way of manning (until recently, there were conscripts in the special forces of the Internal Troops and the special forces of the GU), some peculiarities of training (in particular, as they say, the American special forces, in contrast to the Russian , allegedly, they are not prepared for making long marches on their own two feet - they are thrown by helicopters), but it’s hard for me to answer this question without access to stamped information. If I had access, I wouldn't answer anyway :)
First of all, by the purpose for which it was created. The country's special forces are in line with the country's military doctrine. The US Special Forces, roughly speaking, the attacking one is trained for successful sabotage and capturing people, while the Russian Special Forces is the defender, that is, it is engaged in the release of hostages and ensuring security.