select, pick out
柬 centers on the act of selecting or picking out something from a group, like choosing a specific item from a bundle.
柬 is thought to depict a bundle tied with a string, from which items are selected or picked out. The modern form retains the bundled shape with the central 木 and surrounding strokes.
Picture a tied bundle of sticks with a few sticks sticking out. You reach in and pick out the best one: that's 柬, selecting from a bundle.
For カン, imagine you can pick out the best item from a bundle: can -> カン, and you select it with confidence.