The relative colorimetric intent is like the absolute colorimetric intent in that it clips colors outside the destination’s gamut to the parameter, but the white point is inherited from the destination. Colors that are inside the destination’s gamut are preserved, but their white point is inherited from the destination. The relative colorimetric intent is the 2nd most accurate of the 4, as the colors that are already inside the destination’s gamut do change a little, depending on how different the source and destination’s white points are.
The perceptual intent moves all colors outside the destination’s gamut inward but maintains the distance between colors while doing so. Also, it does this without clipping color to the destination’s gamut. Depending on the content and size difference between the source and destination profile, you could see a large change after the color conversion. This is because all colors are moved. If the source and destination profiles are similar in size, you may see a natural conversion, with no color clipping. If the source is very large, like Adobe RGB, and most of the content is using colors outside the destination’s gamut, you’ll see a large color shift after conversion.
The saturation intent tries to preserve as much saturation as possible. Each CMM handles the saturation intent differently and I don’t recommend using it as the results aren’t predictable.