What is the difference between "flash" and "photographic light" in the studio? What is the use of wireless flash trigger?

The flash is easier to dim the ambient light, and its high power means that you can do more possibilities in the light ratio. For example, things like suppressing sunlight are the patent of flash.

It is easier to obtain high image quality with flash. When the brightness is high, you can shoot with low ISO + small aperture, thus retaining a lot of details. This is quite important in high-end commercial photography.

The photography light is very intuitive. What you see is what you get. It can arrange lighting more quickly and accurately. When the ambient light is dark, focusing under the photography light is more efficient and effective.