In the first image, I rendered it as a pass but it is not rendered with transparency like the 2nd image in which I rendered it without a shadow pass and by holding out the character.
In the first image, you’re viewing the Shadow Catcher pass, and in the second image, you’re viewing the main Combined render that happens to have a shadow in it—the two are different.
When the Shadow Catcher pass is turned off in the pass settings, shadows show up in the main render as black blobs with alpha, meant to be layered over a background. But since they’re just darkness, they can’t capture colored shadows, bounce light, or reflections.
On the other hand, if the Shadow Catcher pass is turned on in the pass settings, the shadows will move from the main render to that white-looking pass, which is meant to be multiplied with the background. Most of the image is 1.0, meaning no change ( 1 • x = x ), some parts are dark (which will darken the background) and some parts are bright (which will brighten the background). With a full RGB shadow image, you can store colored shadows, and by doing a multiplication instead of an alpha-over, you can capture more nuanced effects, like illumination (an emissive object will light up the ground around it) and reflections.