When checking on the box next to an affiliate's name on the Affiliate Overview, two options appear near the top of the page: Approve for all programs and Add to Program. Though they may seem similar, they actually do two very different things.
You can approve an affiliate to a program if they've previously requested to join. This is the button you'd click if you'd like to move an affiliate away from your Pending Program Approval tab and into your Active Affiliates tab.
You can add an affiliate to a program if they weren't a part of it beforehand. When adding an affiliate to a program, they will be automatically approved for that program, and the Assets specific to that program (referral link and marketing assets) will be made available to them.