Message won’t send to non-iPhone user

Is your phone an iPhone? If so, you may use Handoff to send the messages from your iPad via your iPhone as follows.

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

If your phone is not an iPhone, then yes, you must use the phone to send the messages.

Your iPad is not a cellular telephone. It has no capability to send or receive SMS text messages. It can send or receive iMessages to/from other Apple devices.