The Turing machine, and the Turing test are two very different things. They've been both coined by Alan Turing. But a Turing machine doesn't have anything to do with AI. It's a computer that can do any possible maths calculation. But it requires infinite memory. And since nothing is infinite in the real world, it doesn't exist. (Einstein might disagree.)
The Turing test, or "imitation game" is a hypothetical experiment setup. At least it was hypothetical back in the day. It tells us whether some machine can imitate human dialogue well enough to fool someone into thinking they're talking to a human.