What is called a "circular polarizer" in photography is just a linear polarizer combined with a quarter wave plate which converts the linear polarized light that comes out of the first part of the filter to circular polarized light. The conversion to circular polarized light makes the light behave the same as unpolarized in the camera thereby preventing the problems mentioned in WayneF's answer.

To construct an ND filter you can use a linear polarizer and behind that a circular polarizer. The quarter wave plate at the end then converts the linear polarized light that passes through both the filters to circular polarized light, so you are still free of problems.

A circular polarizer in the meaning of a filter that lets through only the left handed or right handed helicity component of light is just what you get if you flip an ordinary circular polarizer. The light then passes through the quarter wave plate first, which means that left handed helicity gets transformed to linear polarized light in one direction while the right handed component gets polarized in the orthogonal direction, the subsequent linear polarizer will then act on that linearly polarized light, it will let through only one component. What is then missing is another quarter wave plate to convert the linear polarized light back to left or right handed polarized light.