Photoshop’s Linear Burn blending mode results in an effect similar to Multiply Mode, where lighter areas in the blend layer allow the bottom layers to “show through,” but is a little different in that it actually darkens the bottom layer’s colors. Here’s the official description:
Looks at the color information in each channel and darkens the base color to reflect the blend color by decreasing the brightness. Blending with white produces no change.
Sounds almost identical to the Color Burn description, except that instead of “increasing the contrast,” Linear Burn “decreases the brightness” and darkens the base layer(s). In fact, unless you have a completely white area on the blend layer, the base layer will always be darkened; using linear burn will always result in a darker picture.
For example, starting with this picture of a rose