The “control panel” is the lower green circuit board in your pic above. It says SAVS20P5 which is a variant of the Honeywell Vista 20P. So your panel is a Honeywell panel. It’s possible that all of your keypads are connected to it, the ADT branded one and the Honeywell ones.
The upper circuit board that says SA5881 is a receiver for wireless sensors.
The white box above it and to the right that says ADT is a cellular communicator that would only work with ADT.
If you wanted to use Surety and Alarm.com with this system you would need a Honeywell System Enhancement Module (SEM) which is another cellular communicator that works with Alarm.com and also enables all the Alarm.com home automation stuff.
Is you door sensor wired or wireless?