Symmetric-cored balls have the same cross section no matter which direction you cut it (along the pin). Set the ball with the pin at the top, cut it in half downward. Both halves are the same.
Asymmetric balls aren't like that. They have more mass on one side of the ball than the other. Cutting the ball on different planes (but still through the pin) will give different views of the core.
Some balls are "dynamically symmetrical", like the Infernos, Buzzsaws, or Fuzes. Different cutting planes give slightly different shapes but they react like symmetric cored balls. Usually four- or eight-sided balls fall into this category.
In reality, it's not so much the symmetry of the core or the mass bias, it's the preferred spin axis. Balls with an asymmetric core and a mass bias have a built-in preferential spin axis. Spin them freely and they will tend to move so that they are spinning about their PSA. The speed at which they move from their initial spin axis to their PSA is an indicator of how strong the mass bias is.
Symmetric-cored balls (or dynamically symmetric as above) don't have a PSA. Asymmetric, mass-bias balls do.
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