Ionization smoke detectors use a radioisotope to generate a very small electrical current, which when interrupted causes an alarm to sound. These types of alarms use a metal–oxide–semiconductor field-effect transistor (MOSFET) to prevent the alarm from sounding, as long as the tiny current is flowing from the detector.
A simple dumbed down version of the circuit, might look something like this.

Notice the 9V battery is connected to the Source contact of the MOSFET, the detector is connected to the Gate, and the Alarm is connected to the Drain. This means that as long as there is a current on the gate, current will not flow from the source to the drain. If something (smoke) interrupts the current flow to the gate, current will flow from the source to the drain and the alarm will sound.
If you add a normally closed switch to the circuit, like so.

Opening the switch will prevent current from flowing to the gate, simulating a loss of current flow from the detector. Which in turn, will cause the alarm to trigger.

So when you press the test button on an ionization type smoke detector, you're not actually testing the circuits ability to detect smoke. Rather, you're testing the circuits ability to react to a loss of current flow to the gate contact of the MOSFET. You're also making sure the battery is not dead, and has enough juice left to sound the alarm if need be.
You should find an installers manual for the main panel and read it thoroughly. But I will give you my thoughts below.
First off, your black wire is connected to the positive terminal not the negative terminal according to your picture and wiring diagram.
Secondly, I am suspicious that this detector ever worked since there is no second wire connected to the power supply terminals. According to the label it takes 12 volts DC to power it and you can't do that with just one wire.
Without seeing any installers manual, I would say the black and white are 12 volts DC power and the red and blue are the common and signal wires.
So test for voltage between the black and white wires. If you get 12 volts move the white wire to the other power supply terminal. Usually the auxiliary contacts would be for another system to be notified that the detector is in alarm. The red and blue should probably go to the ground and signal terminals and the auxiliary terminals are just that, auxiliary. Then see if the detector works.
Notice on the backs of either detector they don't show any wires connected to the auxiliary contacts.
Best Answer
I've seen them triggered by steam, dust, and aerosols (hairspray).
Basically, they are succeptible to small, airborne particles. Most smoke detectors activate when the particles of smoke (or other substances) "block" the detector (which is usually either alpha radiation based or optical).