The difference between positive & negative reinforcements

Positive reinforcements are much more popular and appealing to society today; however, is this because they are actually more helpful or because the term "negative reinforcements" sounds as if one is being punished. Do people actually have an accurate understanding of the differences of positive and negative reinforcements? The authors of our psychology 1001 textbook explain the difference quite simply, "Positive reinforcement could be giving a child a Hershey's Kiss when he picks up his toys; negative reinforcement could be ending a child's time-out for bad behavior once she's stopped whining," (Psychology 213). It is easy to confuse negative reinforcements with the idea that punishment is involved, however, a punishment would decrease the probability of a response whereas the negative reinforcement increases the likelihood of the action occurring again in the future.
I feel like as a child my life was filled with the positive reinforcements: dessert if I finished all of my dinner, an hour of T.V. if I finished my homework, and a new toy if I behaved at my sister's seemingly never-ending basketball tournaments. However, a family that I often babysit for relies heavily on the negative reinforcement: the kids receive dessert if they stop complaining about how much they didn't like dinner, they get to watch barney once they stop complaining about bath time, and they get to go to the park once they stop crying about mom and dad leaving for the night. Looking at both sides of these, I believe that both the negative and positive reinforcements play out equally. Both positive and negative reinforcements demand better behavior from the subjects.