Tilt is vertical swing; swing is horizontal tilt. Tilt and swing change the angle of the lens/film plane.
Shift is moving the lens or film standard left or right horizontally, but still maintaining the same plane. Rise is like shift, but up and down.
Tilt and swing affect both perspective and the plane of the DOF. Usually the front standard is manipulated to affect the plane of the DOF, and the rear standard manipulated to affect perspective, but it is possible to use either standard to do either effect, it's just a method to help keep things straight when you are twisting the camera around.
The perspective effect can be demonstrated in the darkroom by looking at how an enlarger projects an image onto the easel. Raise one side of the easel and that side of the image will stretch out. This is how swing and tilt work.
Shift and rise are used to control what area of the coverage of the lens is positioned over the ground glass/film area. If your lens has lots of coverage, like an 8x10 lens on a 4x5 camera, you could really go crazy. If your lens only barely covers 4x5 (like most press lenses), then you won't be able to rise and shift as much before you encounter the edges of the lens coverage.
What is important is the relationship between the front standard and the rear standard. For instance raising the front standard is the same as lowering the rear standard. Or if you swing the front standard to the left, and then swing the rear standard the same amount to the left, the lens plane and the film plane will be parallel, and the effect would be the same as a rear shift to the right, or a front shift to the left.