Pal,
The difference between the three auto modes is the maximum range and (linked) what aperture you must use. You have a choice of three.
A choice of three ranges, that is. You'll see that with the "red" option, the maximum range (15 m) is more than 4 times the maximum range of the "yellow" option.
What aperture comes with what range depends on the ISO setting (the slider thingy).
So select one of these "A" modes, set the same (!) aperture on the lens, hook the Metz up to the synch contact, and snap away.
But you'll need a cable to do that. The 32CT3 does not have a facility to attach a cable. So you need a hot-shoe-with-cable gadget. These are available from a number of sources.
Just curious: what are you going to mount the 32CT3 on?
Oh, and the rest of the buttons on the 32CT3:
The green thing next to the green battery symbol and the window in the green circle is the battery test.
The "0" and "I" marked buttons on either side of the window below the battery test are the "off" and "on" buttons respectively. The window is the on/off indicator light.
The button next to the thunderbolt symbol is the flash test button.
The window next to it is the "ready" light. When lit, the flash is charged.
Press the test button while aiming the flash at your subject to see if the output at the selected aperture will be enough. A red light above the "TTL" symbol on the left of the mode-selector will light if it will.
It will not light if output is not sufficient, and then you will have yto either move closer, or select a different range, and the larger aperture that goes with it (remember to set that on the lens too!!!)
The mode-selector has the settings you already mentioned.
In TTL mode, the flash expects controlling input from electronics inside cameras, through a SCA adapter. The 500 C/M does not contain such electronics, so you can;t use TTL mode with that camera.
Next to it is M, for manual. The flash will always (!) put out full output. You (!) will have to select the correct aperture for the subject distance yourself. The slider on the unit helps: with it pointing at 100 ASA, for instance, you need f/16 if the subject is 3 m away (from the flash unit!), and f/2.8 if it is 15 m away.
You will have to change aperture every time flash to subject distance changes. The flash does absolutely nothing, other than "giving it all".
If you want to set one aperture and forget about it all, you must use any one of the three "A" (for auto) modes.
Then the flash will control its output automatically, which means it will meter and shut itself down whenever it thinjs enough light has been out out.
Works great as long as you remember 1) to set the correct aperture on the lens as well, 2) remember that there is a maximum range, and 3) not to cover up the flash's sensor (in the front, below the name).