they are standardized
most case fans protocol are using "molex"
psu (power supply units) come in modular, semi modular, or standard (rats nest/cheap) and provide extensions for your fans, sometime the fans daisy chain into a single molex port. the other type of power connector is for sata power (for drives and stuff).
non molex type fans that have 4 lanes are pwm (power watt management). these need to be plugged into the board so that the system can send given amounts of power based on ambient temps or load. i have used molex adapters to these and just put them on open ends on the psu, which unfortunately removes the pwm feature and just has the fan run full blast unless hooked into an external controller.
the mobo fan terminals are dedicated for the cpu usually. it appears u have a gigabyte board, which supports pwm. i only run my case fans from psu, and opt to buy the brand: Noctua now, just my preference
if pwm is a feature you really want, there are some pretty cool fan controllers out there, or just use something simple, cheap, and effective like this one (assuming you have a spare molex power off your power supply open. the pwm connector at the end of the board i linked goes to your mobo system fan terminal (i would plug ur cpu fan directly into the cpu fan terminal on the mobo, and not mess with this adapter except for case fans)
my guess is that the board cant route all that power to all those case fans chained together like that. direct from psu you should be good (edited)