Yes, in the sense that different materials can result in a ball with a different density and weight. For example, the core of a Baseball is typically composed of either rubber or cork. Since rubber is denser than cork, balls made with a rubber core will weigh more than balls made with a cork core. If you were to compare the distance travelled by a ball when hit by a bat, the lighter cork-core ball will travel further than a heavier rubber-core ball (assuming, of course, that all other factors are equal, including the force that the ball was hit with and air drag).
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Yes, it does. But the sports ruling body specifies the composition to very precise degree so that they are pretty much similar.