As Notes and Contacts are updated on the other one almost immediately I assumed it was by Bluetooth, but most texts don't go from phone to iPad. Can I get & send texts on my iPad as well as the phone.
Notes, Contacts, and most of Apple's other apps sync through your internet connection (and iCloud if you are using it). In most ways this is better than Bluetooth, since your devices don't need to be within 40ft (Bluetooth's maximum range) to stay in sync.
Texts are trickier, since you are actually dealing with two different services. Anything sent entirely between iOS devices should show up on both, since Messages will use Apple's own iMessages service.
However, your iPhone acn also use standard SMS from your carrier, and will do so automatically when you send or receive a message from someone who is not on an iOS device.
Since your iPad does not have a cellphone number (one you can receive cell phone calls on), it won't receive SMS messages directly.
Newer iPads and iPhones get around this by re-routing SMS messages received on your phone back through iMessages and to your iPad. This is what rasmith is showing you. I don't remember if the iPad 4 can do this, but can't think of any reason why not.
As you see from the instructions, it has to be enabled in the iPhone's settings.
This also works through your internet connection on both devices.
