Saltwater only:

The easiest way to compare scrubbers to skimmers is to think about food. Food is "organic" and should not to be confused with human food "organic non-gmo food etc" that you eat.

Nutrients, However are "inorganic", and should not be confused with human food nutrients that you eat.

Scrubbers remove inorganics from the water: ammonia, nitrite, nitrate, phosphate, CO2, copper, etc, but do not remove food particles.

Scrubbers add organics to the water: Glucose, amino acids, vitamin C, etc. Oxygen and copepods too.

Protein skimmers, however, do the opposite. That's why they have the word "protein" in the name.

Skimmers remove food particles and copepods from the water, but do not remove ammonia, nitrite, nitrate, phosphate, CO2, copper, etc.

Skimmers add oxygen to the water.

So the only thing in common is that scrubbers and skimmers both add oxygen to the water.