Essentially, iPad can only send email and iMessage (text message for Apple ID or iPhone number).
However if you have iPhone together with iPad, and use the iPhone/iPad's feature called "SMS Relay", you can send them from iPad.
It means you can send SMS/Text for the Receipt, Booking Reminder, Booking Confirmation from the app installed on your iPad.
There are no specific setting in the TapStyle/TapGroom/TapNail/TapPOS side.
Once you set up the SMS relay, you can send Text/SMS from the app.
Please see the following articles (external link) for how to setup SMS relay.
Unfortunatelly, there is no equivalent feature for Android.