The turning point and the climax may be separate, though closely related, or simultaneous events. In The Magician's Nephew, the turning point and the climax are separated by moments. The turning point is when Digory faces off with the Witch, she with darkly stained lips, he with the apple in his pocket. The climax is when Digory realizes the Witch is tempting him to do something nefarious ("You needn't take the little girl back with you, you know") and defies her, effecting everyone's escape from her.
[T]he other things the Witch had been saying to [Digory] sounded false and hollow. And even in the midst of all his misery, his head suddenly cleared, and he said (in a different and much louder voice): "Look here; where do you come into all this? Why are you so precious fond of my Mother all of a sudden? What's it got to do with you? What's your game?" [...] "Up then," said Digory, heaving [Polly] on to Fledge's back and then scrambling up as quickly as he could. The horse spread its wings.
A turning point is defined as the moment when the conflict in the story reaches a crisis resulting in a turning point in the protagonist's actions. It is the crisis at which the protagonist and antagonist meet and challenge each other ("Why do you run from me? I mean you no harm. ... stop and listen to me now,..."). The turning point crisis occurs just before or simultaneously with the climax.
The climax is different from the turning point as it is the result of the crisis. The climax is the point at which the conflict is won (or lost) by the protagonist and at which the outcome of the conflict can be predicted: because Digory sees through the Witch's manipulations and deceits and escapes with Polly and Fledge, it can be predicted that he will return to Aslan with the apple and that Aslan's plans and rewards will go forward, defeating or stalling the antagonist.
[Digory] walked up to Aslan, handed him the apple and said: "I've brought you the apple you wanted, sir."