The adapters are essentially the same.
The second example has 3 pins, but only two are connected.
These adapters will connect fans with three pin ends, but they will run at full speed.
You can slow such fans down by inserting a rheostat, like a zalman fanmate, or a 5 or 7 volt low speed adapter.
The third pin(often yellow) is for a fan speed sensor, and when used in a motherboard connector lets the motherboard sense the fan speed.
A free app like speedfan can report and control such fans.
The 4 pin mobo connectors can handle fans with pulse width modulation such as is found on stock intel heat sinks.
If you plug in a 3 pin fan, it will run at full speed and report rpm to the motherboard.
Some case fans will have 4 pin molex connectors, and some will have 3 pin speed sensing connectors. Some will have both.
Then there are the 4 pin PWM fans which arw usually used on a cpu cooler.