The angle a fisheye lens can capture an angle of about 180 degrees, which is why it's considered an ultra-wide-angle lens. A wide-angle lens can capture an image that is about 100 degrees wide. What this creates is an image that looks like it's been taken through a peep-hole, like those often seen in entryway doors.
Fisheye lenses also have a distinct look, since the outer glass of the lens has a much more noticeable curve than a wide-angle lens. This curve is what allows the lens to capture a greater range of light and create photographs that are wider than your average wide-angle lens.
All DSLR lenses except fisheye lenses are referred to as rectilinear lenses. This is because light travels through the lens in a straight path to the image sensor. This creates the straight lines you see in most photographs.