A protein skimmer removes dissolved organic compounds (DOC) by injecting fine air bubbles that bind to organics and float them out as foam. A filter (HOB, canister, sump with media) handles biological filtration, mechanical particulate removal, and chemical media. Reef tanks need BOTH; freshwater tanks generally need only the filter.
The two systems serve different roles. A skimmer is purely chemical (removes dissolved organics), a filter handles biological + mechanical + chemical filtration.
Reef stocking densities produce more dissolved organics than biological filtration alone can keep up with. The skimmer removes organics directly; the filter (sump, refugium) handles biological conversion of any organics that escape the skimmer. In a 75+ gallon reef, running without a skimmer means accumulating organics that yellow the water and feed nuisance algae.
No. Freshwater doesn't produce the right ionic conditions for foam stability. Skimmers don't work without saltwater's mineral content.
Under 30 gallons you can sometimes skip it with aggressive water changes (15-20% weekly). 40+ gallons benefits dramatically from a skimmer.