1) All Wiccans are neo-pagan but not all (neo-)pagans are Wiccan.
2) Not all Witches are Wiccan and not all Wiccans are witches (depending on who you ask).
3) Not all pagans are witches and not all witches are pagan.
Let me elaborate.
1) Wicca is an area of neo-paganism, brought about in the 1950s by Gerald Gardner. There are also many other pagan/neo-pagan religions such as Asatru, Santeria, Druidism...etc. So as Wicca is a form of neo-paganism, all Wiccans are Pagans/Neo-pagans, just as all Baptists, Quakers, Catholics, Evangelists, etc. are all Christians. But as there are also other denominations of (neo-) paganism then not all (Neo-)Pagans are Wiccan. I hope that helped make things clearer (even if it didn't, I tried!).
2) In order to say whether a Witch is Wiccan or not, we must first define what a Witch is. Some would argue that a witch is simply someone who practices the magick of witchcraft, and religion need not be involved. Others, however, would say that the word witch should only be used to describe Wiccans (or at least Wiccans all should be considered Witches), as Wicca contains a lot of ritual and magick in worship and celebration. Here we have the problem. I think mostly it depends on what you believe a witch is as to how you define them in terms of Wicca/paganism.
Personally, I am quite divided as to which I believe is correct for the reasons I stated above. On the whole I like to use two different deffinitions of "witch". But if we use the term "witches" simply as people who work witches' magick, Wiccans may be witches in their practices, as Wicca is a set of beliefs and not just a practical endeavour.
3) For this part, it's mostly bringing the last two parts together. If you understood the last two parts, then I think it's quite obvious why these two statements are true. You don't have to practice witches' magick to be a Pagan or have pagan beliefs, and you don't always have to have pagan beliefs (although it does sometimes help) to practice witches' magick. So you can be one, the other, both, or none at all :-)
Note: If you want to know the difference between Pagans and Neo-pagans then have a look at my Dictionary page.
Also, I say "witches' magick" as I'm not referring to Ceremonial magick, Chaos magick, etc.
