A UV sterilizer works by decimating the population count of a pathogen in the water. But, it cannot ever completely eliminate the issue. The count of a pathogen is based on the birth and death rate of the organism. A UV helps increase the death rate, but can never drive the population to zero. They can be useful because of the increased death rate, but shouldn't ever be used alone because it cannot completely eliminate the issue. If it is something like ich or flukes, the UV can be used for a few days to decimate the population, and then use medications to finish off the stragglers. On the flip side, they are expensive, use a fair amount of energy, and you have to replace the bulbs often because the intensity of the radiation has to be kept high to do its sterilization, and the flow through the chamber has to be kept clean (no mineral buildup or algae growth on the chamber). They aren't a necessity either, because good fishkeeping practices will keep your tank free of pathogens. The biggest factor here is quarantining any new stock you bring home.
A skimmer removed dissolved organic chemicals from the water, but on;y work for saltwater tanks because the specific gravity of the fluid has to be higher than freshwater. That is, the density of water alone is not high enough for a skimmer to work properly, but the density of salt water is high enough.
