The fighting in Chechnya is pretty brutal, with thousands of part time Chechen men (and a few women) fighting Russians, and other Chechens, for a variety of reasons. But most of the actual fighting is between non-Chechens and Russian commandoes (GRU Spetsnaz.) It's estimated that about 80 percent of the Chechen casualties are inflicted by the Spetsnaz teams, who are the only troops that regularly patrol the mountains where the Chechen rebels and their foreign allies hang out. Most of the dead and captured rebels are not Chechens. They are foreigners, many of them Arabs. There are thought to be only one or two thousand full time rebels in Chechnya.
The Spetsnaz are mostly conscripts, which is in sharp contrast to Western commandos (who are volunteer careerists). But the conscripts were carefully selected and were volunteers for Spetsnaz duty. GRU (Russian Military Intelligence) Spetsnaz brigades do six month tours in Chechnya, suffering about ten percent casualties for each tour. The brigades are under strength, and entire brigades are not sent into Chechnya, so there are only a few hundred Spetsnaz there at a time. The Spetsnaz are there mainly to collect information on the rebels, locating their camps and travel routes. Artillery or bombers are called in to do the actual attacks. When the Spetsnaz do run into rebel units, they inflict far more casualties than they take. But the Spetsnaz patrols do not stop the rebel movements and attacks, only slow them down. There are not enough Spetsnaz to cover the entire province all the time. Moreover, many of the rebel groups (of up to 300 men) use bases outside Chechnya (especially neighboring Georgia and Ingushetia.) While Ingushetia is a part of Russia, Georgia is not, so the Spetsnaz have to move around a lot just to provide some coverage of the entire region.
Russia doesn't send more Spetsnaz to Chechnya because these units spend a lot of time training and are needed elsewhere, especially in Central Asia and for counter-terrorism duty. Moreover, duty in Chechnya is grueling, as the Spetsnaz don't have all the special equipment and specialized helicopters that Western (especially American) commandoes have. Russia also considers their Spetsnaz as a strategic reserve for emergencies, and thus likes to keep at least three of the seven GRU brigades in reserve, training and ready for any unexpected emergency.