Resolution Units:
Scale Factor units are the most intuitive. With a 1x scale factor, the number of points in an image is the same as the number of pixels. At other resolutions, the number of pixels is equal to the number of points times the resolution (so a 128x128 point image at 2x resolution would be 256x256 pixels).
Dots per inch theoretically indicates the number of pixels that would fit in an inch at the given resolution. More realistically, however, 72dpi corresponds to the 1x scale factor resolution, even if the actual number of pixels in an inch on the monitor is different. This means that the dpi resolution is always equal to 72 times the scale factor resolution.
Pixels resolution units show the number of pixels in the image at the given resolution. So a 128x128 point image with a 1x scale factor resolution would have a 128px resolution, while at a 2x scale factor resolution it would have a 256px resolution. If an image's width and height are not the same, the larger dimension is used to determine the pixel resolution. Also, when exporting an image that has Pixel resolution units to a bitmap format that doesn't contain multiple resolutions, only the size for the image will be set, and not its resolution (which will always be 1x or 72 dpi).