Why Do Text Messages Appear on my iPhone But Not My iPad?

To answer this question, it is important to understand the difference between an iMessage and an  SMS text message.

For iMessages to appear on both your iPhone and iPad, both devices need to be setup with the same Apple ID in the Messages settings.

SMS text messages will not automatically appear on your iPad. You need to setup the Text Message Forwarding feature on the iPhone to have SMS text messages forwarded to your iPad.

This article provides additional information to help resolve the issue.