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How do Cryptodira and Pleurodira turtles differ in the way they fold their necks?

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Illustrations of ten representative chelonians, including spiny softshell turtle, Galapagos giant tortoise, green turtle, alligator snapping turtle, Blanding's turtle, common map turtle, eastern box turtle, eastern painted turtle, spotted turtle, and eastern mud turtle, each labeled with its common and scientific name. A scale bar at the bottom shows size comparison. — turtle Turtles (order Testudines).

The primary distinction between the two suborders of turtles lies in the mechanism used to retract the head and neck into the shell.12

Cryptodira: Known as "hidden-neck" or vertical-necked turtles, these animals fold their necks in an S-shape, allowing them to withdraw their heads directly backward into the shell.12
Pleurodira: Known as "side-necked" turtles, these animals cannot retract their heads into the shell in the same manner. Instead, they fold their necks horizontally, laying the head and neck to the side beneath the margins of the shell.31

While both groups possess eight cervical vertebrae, these fundamental differences in neck architecture serve as the primary criteria for their classification.12