1) Young-Earth Creationism
The idea that the days in Genesis 1 are 6 consecutive 24 hour periods, that the Earth and the universe are only 6000 - 10,000 years old.
2) Old-Earth Creationism
The idea that the "6 days" of creation stated in Genesis 1 were extended periods of time. Therefore, we would have an old earth and an old universe but a relatively young human species where all of humanity descends from one man and one woman in just a few tens of thousands of years ago.
3) Deistic and Theistic Evolution
These 2 views hold the position that the earth and the universe are old. The history of life is not one of God supernaturally intervening in direct miraculous ways. Rather, God works through the natural process in a way that is hidden from scientific investigation. They rarely believe in miracles in general.
4) Evolutionary Creationism
This view on creation is similar to that of Deistic and Theistic evolutionists. However, one key difference is that they believe in all the New Testament miracles. They just don't believe that God intervenes in a direct way in the history of life.