You have it upside down!
It can be confusing, because in soil science, sand, silt, and clay refer to sizes of individual particles, but also to soils that have specified proportions of particles of those sizes.
First, let’s identify the size of the individual particles.
Sands are the largest particles we call soil particles. Things larger than sands are called gravels, then cobbles, then stones, then boulders, as the particles get bigger and bigger. But back to the soil particles and their effective diameter:
sand – 0.05 to 5.0 mm
silt – 0.002 to 0.05 mm
clay – <0.002 mm
Sand particles are coarse and gritty, like what you feel on sandpaper. Silt particles are smaller and smooth, much like the feel of powdered sugar or flour. Clay particles are the smallest, and because they are so small, and there are so many more particles in the same mass of sand or silt, clays have a lot of surface area and a lot of attraction for each other. Clays are sticky and cohesive, and are plastic and moldable, much like modeling clay. But when they dry, clays can be very hard – very, very, very hard.
But perhaps this is where the confusion potential arises. A soil with a lot of clay in it will have a lot of aggregates (naturally occurring clumps or clods) in it, and some of these aggregates can be quite large. But these are not individual particles, they are aggregates. And we move from talking about the texture of a soil (relative amounts of sand, silt, and clay) to its structure (how the sand, silt, and clay particles are arranged into aggregates).
Sands have very little cohesion, and so have smaller aggregates, so it may appear sand particles are smaller than clays, but no, it is only a deception.
Remember this order:
from largest to smallest,
sands, silts, and clays,
coarse, medium, fine.