There are 2 definitins for Clay. For a Geologist: - Clay is a naturally occurring material composed primarily of fine grained minerals, which show plasticity through a variable range of water content.
For an Engineer: - Clay is a naturally material composed of fine grains. It does not matter the kind of the minerals. ISO 14688 grades clay particles as being smaller than 0.063 mm.
The clay minerals (from geology point of view) are common weathering products (especially from feldspars) and low temperature hydrothermal alteration. The clay minerals are very common in fine grained sedimentary rocks such as shales, mudstones, marl and siltstone.