So, I can conclude since the photographer chooses the aperture in the TTL mode, the flash increases in output or descreases the flash depending on the aperture the photographer chooses. So the SF20 flash in the TTL mode adapts to the photographers desired f-stop setting.

I think it is clicking.

Matt is this correct?

Close. The exposure isn't determined by how bright the flash output is (it doesn't actually vary), but rather how long the flash fires.

The photographer chooses an aperture and ISO and then sets both on the camera and the flash.

Then, when the photographer releases the shutter, the flash starts firing and the TTL sensor in the camera starts measuring the light from the flash as it bounces back from the subject and goes through the lens. When enough light has bounced back from the subject, the TTL sensor in the camera turns the flash off.

For close distances, the flash duration may be really, really short - e.g. 1/30,000 second.

Even for maximum exposure the flash duration is quite short - 1/400 second.