How should one differentiate between “liquid/slurry without a natural crust” and “uncovered anaerobic lagoon”? Is it dependent on whether the solids are above or below 5%? Or is it dependent on some type of stabilization and treatment with water being deliberately added?

The 5% solids cut-off is a good rule of thumb for many situations. However, it is correct that the best distinction of an anaerobic lagoon is one where there is some treatment and deliberate water addition (ie. If we flush the manure out of the barns, if we add water to vacuum it, if we do SLS, etc.). In a case where the only water added is rainwater and maybe wash water (not flush water), the manure pit is likely best described as a slurry.