A standard alarm input circuit discriminates 3 conditions:
OK - a resistor of 2k2 is present across the terminals. Ideally it should be mounted in series ( some parallel) with the alarm sensor NC contact, and the sensor normally uses a relay that is always powered, so that the inactive state implies the sensor has power.
Short circuit - the cable has been shorted, either by a fault or by deliberate action.
Open circuit - The sensor has detected action that triggers it , either motion, fire or smoke, in the most common sensors used.
The alarm will generally be triggered when armed if the cable goes short or open circuit. When it is disarmed going short will show as a fault, possibly triggering a alarm of system fault if programmed in to the controller. Going open will be displayed as a triggered circuit with no other action.
The tamper switch is used in the same way to add extra redundancy against cable faulting or tampering, and will generally be run in series to all the sensors ( done to save inputs on the panel) with the resistor somewhere in series, generally in the panel in the common lead. It will trigger an always armed tamper signal, and is often not used in residential installs, as it adds extra cores in the cabling.
Alarm controllers are complex systems, generally using a PIC micro ( you can blow the program fuses so you cannot read the eeprom and they are rugged and cheap) with a input using 2 comparators to drive 2 input pins. The system parameters are stored generally in a I2C eeprom that is read at power on, or when programming ( thus there are 2 jumpers to short that allows you to do a factory restore by simply shorting SDA to ground during initial power up) mode is exited. Most allow add on boards and displays to provide extra inputs and a LED or LCD display for programming or operator use ( Those are 100 page programming manuals, with bits you set for options, and can be a little hard to understand the first time round, especially if you are using a set of 11 3mm LED indicators to both set an address and write a bit on or off with the keypad) and for connecting a radio module. Built in modem as well, with auto answer, line cut detection and it disconnects all phones in the house. Built in battery charger, with newer units using PTC fuses instead of glass units. All are designed to operate for 20 years reliably, though the battery will need replacing every 3 years or so.