One difference is in funding. A report by a number of scholars from the National Institute for Early Education Research refers to pre-k as being offered to children who are 3 or 4 years old. It further notes that 27 percent of 4-year-olds nationally are enrolled in pre-k, and 4 percent of 3-year-olds. It goes on to state that 1.3 million children attended such state-funded preschool education. Although the terminologies are mixed, this report seems mostly to refer to pre-k.
One further difference that often separates preschool from pre-k is that pre-k classes are more often attached to a wider school environment, with a path leading through kindergarten to elementary school. Preschools, on the other hand, are more often located in isolation and are not associated in the same way to the wider school setting.
Although the issue is not always clearcut, preschool has a more flexible approach to ages of attendance than pre-k. So, for example, Park Slope Parents -- a website resource for parents -- suggests that ages in preschool can range from 2 until kindergarten age. It also points out that preschools often have more flexibility for attendance, with some only opening for half days and others offering half as well as full-day options.
In some respects preschool may be perceived as either a step between daycare and kindergarten or between daycare and pre-k. Perhaps more importantly, however, preschool is more likely to be an extension of daycare with similarly less-structured activities. Pre-k has more focus on learning as a preparatory step for kindergarten. So attention is given for your child to particular areas of learning, such as using simple math and flash cards as well as structured lessons and activities that promote movement and motor skills.