OK, lets start with a list of the states of matter. In Elementary school, students are usually told that there are three states of matter: solid, liquid, and gas. In Middle school, they are told that there is actually a fourth state; plasma. If they study physics, they learn that there are other states such as Bose-Einstein condensates and Fermionic condensates that only form under very special conditions. None of those seem to fit with our starch and water. Or at least, none of them fit on their own.

What state of matter is wet sand? It is solid sand surrounded by liquid water. Two states of matter mixed together. The same is true for the mixture of cornstarch and water. The cornstarch is not soluble in cold water, so you can think of it as very small, rough sand. When you squeeze the mixture, the solid grains of starch interlock, causing the mixture to behave like a solid. When the mixture is not under pressure, the starch grains separate, and the water lets the mixture flow like a liquid. While the physical properties of the mixture are changing, the water and cornstarch are not changing states. You still have a mixture of a solid and a liquid.

When you read about "Oobleck", most sources talk about non-Newtonian fluids, but fluid is not a state of matter. Water is a fluid. So is air. So is plasma, and even some solids. Fluids flow, so anything that flows is a fluid. Non-Newtonian does not mean that it does not obey Newton's Laws of Motion. A Newtonian fluid always flows with the same viscosity (how easily they flow), regardless of any forces applied to it. Non-Newtonian fluids change their viscosity when subjected to some forces. Again, this is a description of physical properties, but not a state of matter.

When you really look at it, this is not an unusual case. If water bubbles up through loose sand you get quick sand, a mixture that can behave like either a solid or liquid, depending on pressure. What state of matter is meringue? You can explore that with the Egg States video.