There is a difference! Since I have worked in child care and education so long, I never really thought about people confusing preschool with a daycare. I am noticing this more now since I have transitioned from a daycare to preschool.
Preschool is an early childhood program usually for children ages 3-5 although some enroll children a little younger. Preschools usually follow some educational methodology such as Montessori, HighScope or Reggio Emilia and provide some type of curriculum if not incorporated into the methodology. Preschools are only a few hours a day and usually have options from 2-5 days a week. Although preschools are still primarily about play, there is an academic component to it.
Daycare is typically a full day program up to 10 hours and accept children as young as 6 weeks and go up to kindergarten or even school-age children. They are not typically academic focused although some do incorporate a preschool program. Licensing requirements are getting a bit more strict in that they are starting to require more academic focus.
If you are looking for full time care by the week or even by the day then daycare is the route you would go. If you are looking for an environment to prepare your child for kindergarten on a part-time basis then checkout preschools.