I would say that "Paganism" is to a collection of many beliefs stemming from older beliefs that are more nature and multiple deity centered as "Christianity" is to its many denominations.
A "Pagan" is anyone who follows any of these beliefs or religions.
"Neo-Paganism" is integrating modernized thought and technology into older belief systems. It is reconstructionist beliefs reconstructed by use of more modern ideas and tools. Especially since so much has changed through these many hundreds and thousands of years and the way of worshipping in the past is simply not done now.
Therefore, nowadays, with the advent of computers and our many other technological advancements that we take advantage of in the way that we worship, and taking into account the vast diversity that the world presents us with, we are mostly all Pagans utilizing Neo-Pagan methods to follow our various beliefs in Paganism .