Text Message on an ipad

For someone that only has an iPad, and no iPhone, the only thing you could use would be iMessage, or any 3rd party app that would handle messaging, such as WhatsApp. However with 3rd party apps like WhatsApp, both the sender and the receiver would need to have the app. Using iMessage means that both parties need to be using an iOS device, i.e. iPhone, iPad. And yes, an internet connection is required.

By itself, an iPad is limited to internet messaging services only - iMessage, Skype, google hangouts, WhatsApp web (there is no WhatsApp app for iPad), etc.

SMS/MMS require a cellular telephone voice network connection, so an iPad can only use those services when paired with an iPhone via iOS continuity features.