Messages only works with other iOS devices and Macs that are running Mt. Lion or Mavericks. The user that you want to message with, must be setup and registered to use Messages on their devices before you can text with them. You cannot reach them just because they are in your contacts list.
Your phone can send SMS text messages to any other cell phone or smartphone and those texts are not the same as using the messages app. I assume, that's why you can text these people with your phone but not your iPad.