Standard Model:
Quarks are made of quarks... They are the fundamental blocks of all the things that exist in this world. They are indivisible because they are dimensionless.
String Theory:
Quarks are made of bunch of tiny strings that exist throughout 11 dimensions. What I heard was that 4th~11th spatial dimension (excluding time in here), they are extremely small, so small that it rarely interacts with the ordinary 3 spatial dimensions hence we don't feel their existence. Since these dimensions are so small, they manage to fit strings in there. I haven't taken a rigorous course on String theory, so don't take what I said to be 100% fact cause that's just what I heard from the talks of other scientists and physics students. I probably be missing some other important information of the theory.