Approach mode and Skinship are almost exactly the same, but I find Approach mode more enjoyable. Sure, there's nothing like prodding your potential love interest with a stick, but it gets repetitive and awkward in public. Start date. Tap chest. Press and hold on eyes. Slide down bod-- See? That just sounds plain dirty. Try explaining it to your mom or that random person in public watching you play.
In Approach mode, you press (or press and hold) certain buttons to do certain things. When the sakura icon shows up, push the joystick up to activate it. If you do well on the date (good location, answer, and don't make him angry) you get an extra little episode after the date... it's cute but doesn't mean much.
I kind of dislike the new version of Love mode, but it's a lot easier now. It's basically random button pressing really fast until the heart meter goes up. They took away the fun game aspect.