A lightprobe projection is the traditional projections used by Paul Debevec. They are the result of taking a photograph of a scene in a mirror ball. It will wrap an image around the 360 view, however 180 degrees of the view will be distorted and the image will gather to a point. There are less pixels around the edges to capture the outside 180 degrees. This is not a big deal when using the image for lighting.
There also are some very big differences in the absolute values of the pixels in the HDRI. Paul Debevec would set the value of his pixels so the actual value of the light is represented in the color channels. I might call these calibrated probes. In the render world, there are many "HDRI" images available. Some are calibrated to actual values, some are set to values between 0 and others are set to relative floating point values. So the strength of the light can very drastically from one HDRI to another. This can come into play when trying to balance artificial lights or sunlight with various HDRI files. Just not that when changing HDRIs, other lights may also have to change.
Does this help?