I think that @saccharomyces@mander.xyz provided a great response for the specific case of flow in a pipe.

I just want to add that if you look beyond the restrictions of flow in a pipe, there are many other types of behavior that non-Newtonian fluids exhibit. We measure this in the lab on instruments called rheometers. Basically, we put some liquid in the instrument and then deform it and measure the resistance to that deformation. One of the most common ways to apply that deformation is to do so back and forth in an oscillating manner. Depending on the frequency at which you apply this strain, the solid/liquid-like behavior can change. If you have some background in physics or want to get a decent understanding, I found this paper that, on skimming it, seems to be pretty consistent with the way I was taught this stuff in grad school.

One graph I want to point out is Figure 13 which shows what would be a "typical" viscoelastic polymer solution. An easy way to understand this graph is that as we go from left to right, we are applying strain back and forth quicker and quicker, essentially shaking it faster. When the G' value is higher than the G" value, then the material is behaving more like a solid and conversely, when G" > G', then it is behaving more like a liquid. You can see that the material goes through different phases of behavior as the strain frequency changes. Just for you I went and dug up an old graph from my thesis to show a real-life example of this happening too.

My favorite demonstration of this is to put Oobleck (or something similar) onto a speaker and then change the frequency and see what happens.