Foul water is contaminated wastewater from toilets, kitchens, bathrooms and appliances, which needs treatment before it can be returned to the environment. Surface water is clean rainwater run-off from roofs and paving, which can normally be discharged to ground or a watercourse without treatment. The two must be kept separate.
The distinction is about contamination. Foul water carries organic matter, detergents and pathogens, and must be treated in a public treatment plant or an on-site system. Surface water is rainfall run-off and is usually clean enough for direct disposal to ground or a watercourse, subject to controls on silt and hydrocarbons from larger paved areas.
Keeping them separate protects both systems. Mixing rainwater into a foul system overloads treatment plants during storms and can cause surcharge and flooding. Mixing foul water into a surface water system discharges untreated sewage into the environment, which is a pollution offence.