Clay has two distinct definitions, both correct. When referring to clastic sediments, and I think, soils, clay generally relates to the size of the particles. On the Wentworth scale, anything smaller than 1/256th of a millimetre is classified as a clay. Alternatively, a clay is a mineral - a phyllosilicate, as mentioned earlier by Baluncore.
Most clays (soils/sediments/rocks) contain a high to very high percentage of clay minerals, but I have seen analyses where more than 70% of the clay was silica. This is not surprising, given the far greater resistance to chemical and physical attack of silica over clay (mineral).
On the term flocculate, I have only been exposed to this in relation to drilling fluids. These often contain clays, either from drilled formations, or - very often - montmorillonite clay that is added to give the drilling fluid desirable properties. Flocculation in this scenario is the clumping of clay particles in response to the presence of cations, as mentioned previously. I can envisage a similar clumping occurring readily enough in soil