Is a power distribution board just a board that connects all grounds and all positives?
Yes, the power distribution board you linked is, electrically, just connecting the different power and ground supplies together respectively. It appears they also use it as a mechanical frame for a quadcopter.

You can use the LM7805 for your Arduino. The current draw is presumably low, so the linear regulator won't be burning much power. Just note that the linear regulator is less efficient the more current you draw from its output. If your +5V supply will be powering much other than the Arduino, you should look into using a switch mode power supply (buck), as that will be more efficient at higher current draw.