Why foam core? mounting one-dimensional printed images on foam core creates a sense depth and texture and generally looks more polished than a simple piece of paper. Some exhibits that are book heavy do well to mount the labels and descriptive text onto foam core.
Why card stock? When the majority of object on display are already mounted on foam core, mounting your labels on card stock helps distinguish the labels and set them apart as something other than an exhibit object. Color card stock can also be used to draw out or highlight colors in saturated images. In this case, use the card stock to create a frame (1/4" or less) around the image you're displaying.