Occasionally, some people believe they have a problem with their iPad because certain messages appear on their iPhone and not the iPad. Usually, it is not a problem, but rather they are seeing the difference in how iMessages and a regular text messages are delivered.
The Messages app on the iPhone and iPad is capable of sending and receiving regular SMS/MMS text messages as well as iMessages. These two types of messages may appear quite similar to the user, but they operate very differently.
SMS/MMS Text Messages
Traditional text messages are sent through the cellular provider. You can not send or receive regular SMS/MMS text messages on a device that is not connected to a cellular network. Even if your iPad is 3G or 4G capable, it can not send or receive text messages. Your cellular provider delivers text messages based on cell phone numbers. The iPad does not have its own cell phone number.
Understanding iMessage Delivery
With iOS 6, iMessages can be delivered to an iPhone, iPad, iPod touch, and a Macintosh computer running the Mountain Lion operating system. This versatility is because iMessage is related to your Apple ID. Any device that is setup to use your Apple ID is capable of sending or receiving iMessages. If you have an iPhone, the phone number is also associated with your Apple ID and all devices using the Apple ID can receive iMessages sent to your phone number.
When you send an iMessage, Apple will route that message through their servers using an Internet connection. This Internet connection can be either wi-fi or your cellular provider's data network. This allows you to send iMessages from iPods, iPads, and Macintosh computers even without a traditional text messaging plan from a cellular provider.
Many families share a common Apple ID, which allows iTunes or App Store purchases to be shared between everyone in the family. Since iMessages are related to an Apple ID, this can result in iMessages being shared between family members if things are not setup correctly. In addition to the shared Apple ID, each family member should have their own individual Apple ID for use with iMessage and iCloud. Make sure the individual Apple IDs are used in the iMessage and iCloud setup pages for each device. This will allow the sharing of purchases while keeping personal information, such as iMessages, Contacts, and Calendars, independent to each family member.