Apple Users

Look under Settings->Messages.
On my phone, there's a slider to turn iMessage on or off.

Is this what you mean?

On the same menu, there's an option to "Send as SMS" which is the same as old-fashioned texting. It will use cellular data when a wifi network is not available (I think) --- It says "Send as SMS when iMessage is unavailable. Carrier messaging rates may apply"

Also, under settings->cellular, there's a slider to turn off cellular data (useful when abroad, since in many countries, cellular data will cost a lot --- depends on your plan)

This *is* kind of complex.
The other day, the phone rang and the call showed up on the iPad, which was a bit surprising, and it went smoothly.