A:Answer The AT&T (or other carrier) models have their own cellular service for internet in addition to WiFi. Like a phone. In other words as long as you have cellular signal from your carrier you can access the internet from anywhere. The Wifi models can only access the internet when connected to a wifi hotspot such as in your home, work or other location that has free or paid wifi.
With respect to your second question, as far as I know you cannot directly receive regular text messages (SMS) on any ipad, regardless of whether it is a carrier model or wifi only. It is not a phone. You can however receive and send iMessages which are to and from Apple devices only. There are also services such as "Continuity" from Apple which will allow you to send and receive SMS messages on your iPad by relaying them to and from your iPhone.
Hope this helps.