How is the Turing Test meant to be different from a test of math problems, or chess, or some other game?

a$.$ The Turing test is used to find an AI that will be able to surpass human performance in all math problems and in any possible game without that AI being designed for one specific set of rules; specific tests only test for an AI that surpasses humans in one specific category.

b$.$ The Turing test is different from a math test or chess test because there are no rules in the Turing Test; however, there are many and varied rules in a math test or in a chess test.

c$.$ The Turing Test is meant to test for conscious experience in an AI or computer; whereas a math test or chess test is only used to test for intelligence and learning capacity in an AI or computer.

d$.$ The Turing Test is meant to test general intelligence as opposed to specific intelligence. It is meant to show that a computer is capable of dealing with the complexities of natural language interactions, complexities that require a high degree of adaptability, pattern recognition, and understanding in a broad range of areas.