5V signals from the Arduino should work with either of those boards. The difference is that the 5V board needs a 5V power supply (on the VCC pin) to drive the coils and the 12V board needs a 12V power supply. There should be about a 30% leeway though; e.g. a 9V supply should still work with the 12V board.
Here's a tutorial for relay boards.
Note that your 8 relay board has optoisolation (the small, black, 4 pin rectangles on the board). The 4 relay board does not. See above tutorial for more details on that.
(overlapping Krodal's reply but too lazy to adjust the parts of mine that restate what he said 