Pre-filtration is the filtration that takes place prior to water entering the tank. These are typically gravity fed filter systems. Pre-filtration is typically the only filtration required when using the collected rainwater for irrigation.
Post-filtration is the filtration that takes place after the collected rainwater has left the tank. Post-filtration systems are typically a pressurized system that filters to a much lower number of microns than typical pre-filters. Post sediment filtration and disinfection is usually required anytime the water will be used for indoor use such as flushing toilets, washing clothes, or shower usage.