Why can’t I get all the same messages on my iPad that I get on my iPhone?

Your iPad is not a cellular telephone. It has no ability to send or receive SMS messages, only iMessages.

What is the difference between iMessage and SMS/MMS? - Apple Support

However, if you wish, you may set up Text Message Forwarding to let your iPad access messages from your iPhone.

How to forward SMS/MMS text messages from your iPhone to your iPad, iPod touch or Mac - Apple Support

Simplest way is turn on messages in iCloud on all devices using your iCloud account. See -> Use Messages in iCloud - Apple Support