No, the Sicilian Defense is not played by one player or the other. The Sicilian Defense is the position that occurs after the moves 1.e4 c5.
The Sicilian Najdorf is the position that occurs after the moves 1.e4 c5 2.Nf3 d6 3.d4 cxd4 4.Nxd4 Nf6 5.Nc3 a6.
It is not "White" playing the Sicilian Najdorf and it is not "Black" playing the Sicilian Najdorf. The opening as a whole is the Sicilian Defense, Najdorf Variation.
If any of White's first 5 moves, e4, Nf3, d4, Nxd4, Nc3, or if any of Black's 5 moves, c5, d6, cxd4, Nf6, a6, are different, you do not have a Sicilian Najdorf. It is a common mistake for players to say "Black is playing the Najdorf". No, Black is not playing the Najdorf. The entire game is a Najdorf.
If you say "Black is playing the Najdorf", then what you just told me is that 1.d4 c5 2.e4 d6 3.h3 cxd4 4.g4 Nf6 5.a4 a6 is a Najdorf because Black played the same 5 moves. Not true at all! This is just some sort of garbage with both sides playing random moves.
An easier example. 1.e4 e6 2.d4 d5. This is a French Defense. Black did not play the French. The opening as a whole is a French Defense.
1.d4 e6 2.c4 d5 is not a French, despite Black playing the same 2 moves. It is a Queens Gambit Declined.
So there is no "Black is playing the Sicilian" or "White is playing the Sicilian". The moves 1.e4 c5 define the Sicilian, regardless whether Kasparov, Anand, Topalov, or someone's senile grandmother plays 1.e4 with the White pieces or 1...c5 with the Black pieces. Both moves must occur for it to be a Sicilian Defense.
When I see what top players like Anand/Kasporov play as white I see Sicilian, But from my understanding Sicilian defence is played as Black. Is it like playing against Sicilian?