The difference is that there is a process in place with court oversight, and a judicial system which isn't completely beholden to the government.

Even with the most egregious abuses of these National Security Letters, their scope is still limited and they have to have justification for whatever they demand. There is a record of such letters, which can be examined, for example by politicians in congress or the next administration. Companies can even challenge these letters. And they are still leaked all the time.

I doubt it works that way in Russia.