There’s always a lot of confusion about what rendering intents are. They exist because printers (the machines) usually can’t produce as much color gamut as a light-emitting monitor can. There are various ways to shrink a highly saturated image to fit into a print and those ways are what we call Rendering Intents.
There are two rendering intents that photographers use: Relative Colormetric (with BPC), and Perceptual.
Relative Colormetric simply pulls down the high-saturated (out of gamut) colors in the image to their nearest printable color and leaves the in-gamut (less saturated) colors of the image alone.
Perceptual pulls all the colors down in saturation in relation to each other. This means the most saturated color in the image will be pulled to its nearest printable color and all the colors that are slightly less saturated in the image will also be pulled down a little bit so the “color contrast” or “color relationships” are maintained in the image. This was good for low-gamut printers about a decade ago.
Because the newer printers have so much color gamut now, most everyone is able to print with Relative Colormetric intent and that has become the default.
Cheers and happy Saturday!