Silver - These will walk off the cliffs and will sometimes bump into Yoshi where he's standing. It will stay on the cliff in Yoshi's Island DS.
Pink - These will walk off the cliffs like the silver one in its first appearance. In Yoshi's Island DS, it'll walk off the cliff.
The only way to defeat a Tap-Tap is to let it fall off the botomless pit and let it crash into another one. Some Tap-Taps will hop, making it difficult for Yoshi to pass. However, underestimating it is a threat in the early and later levels. Using a quick egg will send one flying backwards, and if it hits another one, it will be crushed.