ADT Tools is custom code. You have to add a copy of it to your own account and then publish it to yourself. This only works with the classic app. Here’s the FAQ on that process and the terminology used, which should help you in further discussions. 
Smart Home Monitor is an official feature, but the way it works when you have the ADT model of the hub is a little different, so I will leave that to @Mavrrick58 to explain.
Also, it’s important to note that there are two completely different features with different options that are both called smart home monitor, one for the classic app, and one for the new app. You can run both apps at the same time, but automations you set up or notifications that you receive from smart home monitor in one will not in any way affect the other, which can get pretty confusing. Also be careful to note in each conversation about SHM whether the person is talking about the classic app or the new app.