Newtonian fluids flow faster as you increase the pressure on it. A non-Newtonian fluid flows slower or becomes more viscous.
A good example is a paste of cornstarch in water. The harder you push...
The most common method of classifying fluids are through a measure of viscosity; how close to being soilid. Peanut butter would have a very high viscosity, where gasoline or water are very low....