Go into your settings-messages-send a receive on the iPad and make sure it is set to whatever your iPhone is set to send and receive address is. Your phone number or your email address you have set to it. If it happens to be your phone number and it's not showing up as an option on your iPad, sign out of your Apple ID on the same screen and then sign back in. You should see the phone number come out as an option now
When you say that both device are set correctly, are you saying that both devices are setup with the same iCloud account? Yes, I am asking for a reason. Make sure that the send & receive option in the iMessage settings is the same on both devices.
Make sure both device have phone # or email added.
I use Phone # only on all devices... This eliminates confusion which is caused with using both email and Phone # .... Quite often it creates two separate messages.