That is a great question. From what I have seen and experienced, the terms preschool and Pre-K are often interchangeable. You will sometimes see Pre-K 3 and Pre-K 4 to distinguish between what age level the class is designed for. Day care is a program that offers child care services that does not necessarily have an educational component. It offers great benefits such as social interactions, learning through play and gaining self-help skills but academics may not be a focus. In addition, day care programs can start as young as 6 weeks old while preschool/Pre-K starts at age 3 (or 4 depending on the school). If you are looking for a program for a 3 or 4 year old, I recommend looking for a preschool not a day care. Some preschools offer day care before or after but you want a program that offers an academically enriched program as to prepare your child for Kindergarten. When looking for a program, ask about their curriculum and class routine. Also, it is best to find a program that has a certified teacher as the lead teacher or at least on staff to help develop and implement the curriculum. I hope this helps!